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# Complex Numbers

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The complex numbers a and b satisfy $a \overline{b} + 2 - 8i = -1 + 5i$.  Find $\overline{a} b - 5 + 7i$.

Apr 22, 2021

$$ab+2-8i=-1+5i$$  is also equal to $$ab=-3+13i$$ and then you would have a new equation of $$-3+13i-5+7i$$
So your answer would be $$-8+20i$$