Consider the complex numbers:

z1 = 3 + j and z2 = −5 + 5j

(i) (2 pts) Plot both numbers on the complex plane.

Answer:I have done.

(ii) (2 pts) Evaluate |zi| and angle zi for i = 1, 2. *i is a subscript

My attempt: I know that |zi|is the magnitude and is bascially the square root of z x z*. But here we have z1 and z2. So what is zi. Are we supposed to combine z1 and z2 and then take the magnitude. Please give me a headstart on this problem.

(iii) (2 pts) Without using a calculator, show that angle:z1 and angle

z1 + z2) differ by an integer multiple of pi/2.

My attempt: So I know the angle is arctan of y/x. I dont know how to prove this without a calculator. Please help on this also.