SOLUTION: Perform the complex number operations and write the answer in the a + bi form. 2i + (3 - i) / (2 + 5i)

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Question 186575: Perform the complex number operations and write the answer in the a + bi form.

2i + (3 - i) / (2 + 5i)



Answer by ankor@dixie-net.com(12692) About Me  (Show Source):
You can put this solution on YOUR website!
Perform the complex number operations and write the answer in the a + bi form.
2i + (3 - i) / (2 + 5i)
;
assume it's
2i + %283-i%29%2F%282%2B5i%29
over a single denominator
%282i%282%2B5i%29+%2B+%283-i%29%29%2F%282%2B5i%29 = %28%284i+%2B+10i%5E2%29+%2B+%283-i%29%29%2F%282%2B5i%29 = %28%284i+%2B+10%28-1%29%29+%2B+%283-i%29%29%2F%282%2B5i%29 = %284i+-+10+%2B+3+-+i%29%2F%282%2B5i%29 = %283i+-+7%29%2F%28+2%2B5i%29
Multiply by the conjugate of the denominator over itself:
%283i+-+7%29%2F%282%2B5i%29 *%282-5i%29%2F%282-5i%29 = %286i+-+15i%5E2-14+%2B+35i%29%2F%284+-+25i%5E2%29 = %286i+-+15%28-1%29-14+%2B+35i%29%2F%284+-+25%28-1%29%29 = %286i+%2B+15+-14+%2B+35i%29%2F%284+%2B+25%29 = %281+%2B+41i%29%2F29