Question

Find the complex number z that satisfies (1 + i)z - 2 overline{z} = -11 + 25i.

Im not sure how to solve this. I tried distributing the z out first but im still confused on this problem.

Answer 1

If z = a+bi, we have

(1+i)(a+bi) - 2(a-bi) = -11+25i
Expand all that out and you get

(-a-b)+(a+3b)i = -11+25i

So, that means that

-a-b = -11
a+3b = 25

a=4
b=7

So, z = 4+7i