complex no (1 Viewer)

[martin310015]

can someone tell me how to do this
Z element of C such that Re(z)=2Im(z), and z^2-4i is real. find z

do i let z=x+iy
and say that x=2y
(x+iy)^2(-4i)=x^2-y^2+2xyi-4i......got stuck

 

[Heinz]

z = 2y + iy
z² = 4y² + 4iy² + i²y²
= 3y² + 4iy²
z² - 4i = 3y² +4iy² - 4i
= 3y² +4i(y² - 1)

y² = 1
:. y = +/- 1 (subbing back in to z = 2y + iy)
:. z = +/- (2+i)

 

[martin310015]

not as hard as i thought......anyway thanks heinz