Question

plse solve this sum

Answer 1

An obvious solution to the equation is that one of the complex numbers is zero, but this makes the argument(s) undefined, so we can skip that solution. The remaining non-zero solutions can be found by expanding the equation explicitly, so if we call \(z_1=a+bi\) and \(z_2=c+di\), the first equation (|z1+z2|=|z1−z2|) is equivalent to the condition
\[ac+bd=0\]
That expression maybe rings a bell, namely that it is the real part of the product of the first complex number by the second numbers complex conjugate. So we have \(Re(z_1\bar{z_2})=ac+bd=0\). This of course also means that \(\arg z_1\bar{z_2}=±\frac{π}{2}\) (the product lies on the imaginary axis). With this help you can most likely do the rest by yourself, if you remember the rule for dividing complex numbers.

Answer 2

Now it's all sound, I made an error when writing my scribbles here first.

Answer 3

okay

Answer 4

argz1-argz2=+-pi/2

Answer 5

That's right :)

Answer 6

thanks @dape