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.
