Question

Solve for z, and give your answer in the form a + bi

Answer 1

The answer is z = 3 + i

z = a + bi
conj(z) = a - bi

conj(7 + 3i) = 7 - 3i

(conj)z + 2z = 2 + 4i + conj(7 + 3i)
a - bi + 2(a + bi) = 2 + 4i + 7 - 3i
a - bi + 2a + 2bi = 2 + 4i + 7 - 3i
3a + bi = 9 + i

From here:
3a = 9        and      bi = i
a = 9/3                   b = i/i
a = 3                       b = 1

z = a + bi
z = 3 + 1 * i
z = 3 + i