If |z1 + z2| = |z1 - z2|, prove that the difference between the arguments (of z1 and z2) is pi/2.

I'd be grateful for any help or pointers in trying to prove this please. Thanks.

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- April 2nd 2008, 11:54 AMnmanik90argument of a complex number
If |z1 + z2| = |z1 - z2|, prove that the difference between the arguments (of z1 and z2) is pi/2.

I'd be grateful for any help or pointers in trying to prove this please. Thanks. - April 2nd 2008, 12:08 PMania
write them down as exponential funcitons: z1=r1*exp(i*phi1)

calculate the |z1+z2| by multiplying by the same with -i instead of i

r1 and r2 all fall out

it stays exp(i*(phi1-phi2)) = - exp(-i*(phi1-phi2))

divide by exp(-i*(phi1-phi2))

now it's exp(i*2*(phi1-phi2)) = -1

so phi1-phi2 must be pi/2 because exp(i*2*pi/2)=exp(i*pi)=-1