SOLUTION: Select any imaginary number (of the form "a + bi," where a and b are non-zero real numbers), and another number such that the sum, difference, product, or quotient of the two numbe

Algebra ->  Algebra  -> Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Select any imaginary number (of the form "a + bi," where a and b are non-zero real numbers), and another number such that the sum, difference, product, or quotient of the two numbe      Log On

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Question 190594This question is from textbook
: Select any imaginary number (of the form "a + bi," where a and b are non-zero real numbers), and another number such that the sum, difference, product, or quotient of the two numbers is a real number.
Am very lost here. Thanks!This question is from textbook

Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
It turns out that ANY number of the form a%2Bbi added to it's complex conjugate of the form a-bi is


%28a%2Bbi%29%2B%28a-bi%29=%28a%2Ba%29%2B%28bi-bi%29=2a%2B0i=2a


So adding ANY complex number to it's complex conjugate results in a real number.


Example:

Let's pick the number 2%2B3i (where a = 2 and b = 3) and add it to it's complex conjugate 2-3i to get


%282%2B3i%29%2B%282-3i%29=%282%2B2%29%2B%283i-3i%29=4%2B0i=4


In short %282%2B3i%29%2B%282-3i%29=4


Note: it turns out that multiplying a complex number by it's complex conjugate also results in a real number (division is a different story however).