21. Given that z is a complex number satisfying |2z - 1|=|z2|, prove that |z| = 1 by: (a) letting z = x+iy, (b) squaring the equation and then using the result |z|2= zz.

2. Let w = f(z) = z² be a complex function. Use the Cartesian representation of complex numbers to write f(z) = u(x, y) + iv(x, y). Find the values of w that corresponds to (a) z = i and (b) z = –2i, and show them graphically.

solve every problems given and provide the corresponding answer/s needed.

2.-Find the following complex function u (x, y) and v (x, y)