Question

Anybody know the answer to this?

Answer 1

First multiply

then add

4+3i/5+2i

Answer 2

First distribute the top:

(2 - i) * (1 + 2i) = 2 - i + 4i - 2i^2 = 4 + 3i

Now, we have (4 + 3i)/(5 + 2i). We have to multiply by the complex conjugate of the denominator, which would be 5 - 2i:

{(4 + 3i) * (5 - 2i)}/{(5 + 2i) * (5 - 2i)} = (20 + 15i - 8i - 6i^2)/(25 - 4i^2) = (26 + 7i)/(25 + 4) = (26 + 7i)/29 = 26/29 + 7i/29

Your answer is:

26/29 + 7i/29.