Question

复数z=[(1+i)^3(a+bi)]/(1-i)(a,b属于R)且|z|=4,在复数平面内,z所对应的 点在第一象限,

Answer 1

角XOZ=30度, |z|=4, z = 2根号3 + 2i

(1+i)^3 (a+bi) / (1-i) = 2根号3 + 2i

-2 (a+bi) = 2根号3 + 2i

(a+bi) = -根号3 - i

a = -根号3, b=-1