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Abstract algebra is a branch of mathematics that studies algebraic structures, such as groups, rings, fields, and vector spaces. It is called "abstract" because it focuses on the properties and relationships of these structures, rather than their specific representations in the form of numbers or functions.



In abstract algebra, algebraic structures are defined by a set of elements and operations that can be performed on those elements. For example, a group is a set of elements with a binary operation (usually denoted as "" that satisfies certain properties, such as associativity and the existence of an identity element. A ring is a set of elements with two binary operations (usually denoted as "+" and "" that satisfy certain properties, such as the existence of an identity element for each operation and the distributive property.



Abstract algebra is used to study the properties and relationships of algebraic structures and to understand their abstract properties, rather than their concrete representations. It is an important branch of mathematics with many applications in areas such as cryptography, computer science, and physics.

https://solvedhomework..com/2022/12/abstract-algebra.html

A complex number is a number in the form a + bi, where a and b are real numbers and i is the imaginary unit, which is defined as the square root of -1. The real part of the complex number is represented by a, and the imaginary part is represented by b. For example, 3 + 4i is a complex number, with a real part of 3 and an imaginary part of 4. Complex numbers can be represented graphically on the complex plane, with the real part of the number being the horizontal axis and the imaginary part being the vertical axis. Complex numbers can be added, subtracted, multiplied, and divided using the rules of algebra, just like real numbers. They are used in many areas of mathematics and science, including electrical engineering and physics.

How to solve complex numbers
There are several ways to solve complex numbers, depending on the problem you are trying to solve. Here are some common techniques:

Adding and subtracting complex numbers: To add or subtract two complex numbers, you can simply add or subtract the real parts and the imaginary parts separately. For example, to add 3 + 4i and 5 + 2i, you would add the real parts (3 + 5 = and the imaginary parts (4 + 2 = 6) to get the result 8 + 6i.

Multiplying complex numbers: To multiply two complex numbers, you can use the distributive property and the definition of the imaginary unit. For example, to multiply 3 + 4i and 5 + 2i, you would distribute the first number over the second like this: (3 + 4i)(5 + 2i) = 35 + 32i + 4i5 + 4i2i. Then, you can simplify the expression using the definition of the imaginary unit (i^2 = -1): 35 + 32i + 4i5 + 4i(-1) = 15 + 6i - 20i = -5 + 6i.

Dividing complex numbers: To divide two complex numbers, you can multiply the numerator and denominator by the complex conjugate of the denominator. The complex conjugate of a complex number is obtained by changing the sign of the imaginary part. For example, to divide 3 + 4i by 5 + 2i, you would first find the complex conjugate of the denominator: 5 + 2i becomes 5 - 2i. Then, you would multiply the numerator and denominator by the complex conjugate: (3 + 4i) / (5 + 2i) * (5 - 2i) / (5 - 2i) = (15 - 8i) / 9 = (5 - 2.67i).

Solving equations with complex numbers: To solve an equation involving complex numbers, you can use the same techniques you would use to solve an equation involving real numbers. However, you need to be careful to keep track of the real and imaginary parts separately. For example, to solve the equation (3 + 4i)x = 8 + 9i, you would divide both sides of the equation by 3 + 4i to get x = (8 + 9i) / (3 + 4i) = (8 - 4i) / 5 = 1.6 - 0.8i.

I hope this helps! Let me know if you have any questions.

https://solvedhomework..com/2022/12/complex-number.html

To find the x-intercept of an equation, set the y-value equal to 0 and solve for x. This will give you the value of x at which the line crosses the x-axis. For example, consider the equation y = 2x + 1. To find the x-intercept, set y equal to 0 and solve for x:



0 = 2x + 1

-1 = 2x

x = -1/2



Therefore, the x-intercept of this equation is (-1/2, 0).



To find the y-intercept of an equation, set the x-value equal to 0 and solve for y. This will give you the value of y at which the line crosses the y-axis. Continuing with the example above, to find the y-intercept, set x equal to 0 and solve for y:



y = 2*0 + 1

y = 1



Therefore, the y-intercept of this equation is (0, 1).



I hope this helps! Let me know if you have any questions or if you'd like further clarification

https://solvedhomework..com/2022/12/finding-x-and-y-intercepts-of-equation.html

Nairalanders please I have been making research on tuition free universities in Germany and I've found a lot of them but I can't find any course that does not require language proficiency, please anyone should help on the process of application.
Thanks

A woman, her ex husband and the man who used to be her lover were all invited on a radio show to discus the paternity of a child After the show host had grilled all of the parties involved in the issue, it was found out that the woman got pregnant for her love while still married Many Nigerians who watched the recorded version of the show were surprised at the woman's perceived disloyalty .

A radio show hosted by a popular presenter, Oriyomi Hamzat, has revealed how a married woman got pregnant for another man. In a video shared on Instagram, Oriyomi quizzed the husband, the woman, and her lover on the issue to find out the paternity of the child involved.



A video has shown the moment a woman revealed how she got pregnant for another man. Photo source: @agidigbo887fm Source: UGC He is not the father The woman said that after she left her husband, she moved in with her lover and married him. The ex-husband on the other hand said that while they were still married, the woman was always calling her lover a brother.
The ex-husband said that he is not concerned about what had happened in his home, that he just wants to get his son. According to the man, he never knew the his former wife was in a relationship with the lover. He was surprised when the woman without mincing words said that he is not the father of the said child.







View this post on https://legit-ng..com/2022/08/hes-not-father-woman-gets-pregnant-for.html

Please can anyone help with cost and requirement for starting up a reality tv show in Nigeria.

Please can anyone help with cost and requirement for starting up a reality tv show in Nigeria.

The vice-chancellor of the University of Lagos (UNILAG), Akoka, Oluwatoyin Ogundipe, has hinted that the suspension of the nine-month-old industrial action by the Academic Staff Union of Universities (ASUU) may not be enough to guarantee the much-anticipated return of smooth academic activities to the universities nationwidee.

Mr. Ogundipe, who was recently reinstated after he was controversially removed from office by the dissolved Wale Babalakin-led governing council, hinted of a possible complete blackout in many of the higher institutions over the hike in electricity tariff by the power distribution companies.

The professor of Botany, who stated this at a forum last week, said his university that used to pay monthly charges of N61 million when academic and non-academic activities were in full capacity recently paid N62 million for the month of November 2020.

He said; “During the total lockdown when there were no activities apart from home use for workers living on the campus, we were paying N32 million on a monthly basis. But now without the students on the campus, we were charged N62 million for November. This implies that the amount may double when students are back on the campus and the activities resume fully. How can we afford that?”
Read full story here http://nbw.com.ng/high-electricity-tariff-may-cripple-nigerian-universities-unilag-vc-ogundipe/

Liverpool manager Juergen Klopp sees no reason why Mohamed Salah would want to leave the Premier League champions but says he would not keep the Egyptian forward at the club against his will.

Salah told Spanish newspaper AS in an interview this month that he admired Real Madrid and Barcelona, fuelling talk in the British media that he was looking to move on.

“I think the only reason to leave Liverpool at the moment is the weather. What other reason could be there?” Klopp said at a news conference

This is one of the biggest clubs in the world, we pay good money … we have a sensational stadium with outstanding supporters.

“You cannot force people to stay but that is it … We make changes and bring players in and if a player wants to go then we cannot, probably not hold him back; it’s just that I would not understand why somebody would want to go.”
Read full story http://nbw.com.ng/liverpool-wont-force-salah-to-stay-says-juergen-klopp/

More members of the Peoples Democratic Party in the House of Representatives have faulted the threat by the leadership of the House to sanction the leader of the PDP caucus, Mr Kingsley Chinda, over his call for the impeachment of the President, Major General Muhammadu Buhari (retd.).

Chinda had urged Nigerians to prevail on the National Assembly to begin the impeachment process against Buhari over the killing of 43 rice farmers in Borno State by Boko Haram and the abduction of over 340 schoolboys in Kankara, Katsina State.

But the Majority Leader, Alhassan Ado-Doguwa, had in an interview with journalists in Abuja on Monday, threatened Chinda with sanctions by the House if the PDP leader continued to call for Buhari’s impeachment.

A member from Rivers State, Mr Awaji-Inombek Abiante, in an interview with our correspondent on Wednesday, however, stated that Chinda had not committed any offence by speaking for his constituents and other Nigerians as their representative.

Abiante dismissed the threat as “a lack of understanding of the responsibilities of a legislative arm of government,” adding that it exposed the “lack of depth.”

Responding to a question on whether members of the PDP caucus were out to defend Chinda, Abiante said, “Does the House have the power to send a member elected by the people of a constituency out of legislative functions? The answer is no. If in the past, people have been so barred, my people elected me to be in the House and I speak on their behalf. Nobody has the right to take me out.”

Chinda had, in his reaction to Ado-Doguwa’s threat, said he was ready to face the consequence of the impeachment calls. “I’m prepared,” he had told our correspondent.

The PDP leader had added in part, “You should ask if it would be fair to Nigerians. I speak for Nigerians. They should ask Nigerians to stop the call for the removal of President. I have the backing of the majority of Nigerians.”

Another PDP member, Farah Dagogo, representing Degema /Bonny Federal Constituency in Rivers State, had also chided Ado-Doguwa for “playing to the gallery.”

Dagogo said the Majority Leader, who was also a legislator in the defunct Third Republic, “ought to be experienced enough to know that Kingsley Chinda did not commit any legislative infraction with his patriotic call.”
Read full story here http://nbw.com.ng/buharis-impeachment-more-pdp-reps-tackle-house-leadership-over-sanction-threat/

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A 43-year-old man, Sylvester Ehiarinmian, is presently under the custody of the Zone 2 Police Command, Onikan, for allegedly swindling a United States based Nigerian woman of several millions of naira and landed properties located in some parts of Nigeria.

The victim, Mary Ope, a 40-year-old married woman with children, who owns a farm in the Federal Capital Territory, FCT Abuja, reportedly had the intention of setting up other businesses back home.

She was said to have been introduced to Ehiarinmian, as capable of providing her with security to and from the farm.

According to the Assistant Inspector-General of Police in-charge of the Zone, AIG Ahmed Iliyasu, on Wednesday, September, 16, 2020, the suspect was said to have made a love advance to her, with a promise to marry her, even though she claimed he was aware she was married. She hypnotically fell in love with the suspect who dispossessed her of both cash and property.

Ahmed revealed that the the suspect obtained the sum of $15000 dollars (N5.8m) from her, to procure visa for the victim’s sister, another $10,000N3.8m) he proposed to purchase carpets for an office they both agreed to operate and N40 million for the establishment of a medical laboratory.
read full story https://www.9jaolofofo.com.ng/2020/09/man-swindles-his-us-based-nigerian.html?m=1

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