Write the complex number in polar from.

Solve the system of equations Re (z₂) = 0, |z| = 2.

Find the complex number satisfying the equation

If z and w are two complex numbers such that |zw| = 1 and arg (z) – arg (w) = π/2, then show that

Fill in the blanks of the following

For any two complex numbers z₁, z₂ and any real numbers a, b, |az₁ – bz₂|² + |bz₁ + az₂|² = ….