NEED HELP WITH A QUESTION z^2 - i (1 Viewer)

[Living It Up]

ok i attemped to do this question about seven time now wit on lck, i finished of all the questions in the exercise but still coundnt do this one ... i have like a mental block when ever i see this wuestion anyway to the pll who would like to help the question is

Solve z^2 - i ( it's prob really easy but i cant seem to do it )

thanks alot

 

[spice girl]

Well you can't solve anything unless you have an equal sign somewhere so I'll assume z^2 - i = 0

so z^2 = i

|LHS| = |RHS|
so |z^2| = 1
|z| = 1
let z = cis(x)
so z^2 = cis(2x) = i = cis(pi/2)
2x = pi/2 + 2k*pi
x = pi/4 + k*pi (k = 0,1)
so z = cisx = cis(pi/4), cis(pi/4 - pi) = (+-) (1 + i)/sqrt(2)

 

[Living It Up]

Thanks alot ....i cant believe i couldnt do that ... arrghh i knew it was something simple but yea ... thanks again and just out of curiosity... hve u all ready finished ur HSC or are u in yr 12 this yr ???

 

[ND]

cis(x) = cos(x) + i.sin(x)