Hi Office_Shredder,
If I make z1=a and z2=bi, then both the sum and the difference of both look like a complex number and its conjugate respectively. Also, |z1+z2|=|z1-z2| .
z1/z2 then becomes a/bi. Multiplying top and bottom by bi produces -(a/b)i, which is only imaginary.
Is this correct?
Two complex numbers z1 and z2 are taken such that |z1+z2|=|z1-z2|, and z2 not equal to zero.
Prove that z1/z2 is purely imaginary (has no real parts).
I started by taking z1=a+bi, and z2=c+di, then z1+z2=a+c+i(b+d) and z1-z2=a-c+i(b-d)
|z1+z2|=√(a+c)^2 + (b+d)^2
|z1-z2|=√(a-c)^2 + (b-d)^2...