college mathematics

1. Let z be a complex number which satisfies the following equation: 23+ 123 - 32-4 = i. (a) (2 points) Show that z can not be a real number. 1 - 41 (b) (4 points) Find the modulus of (23 + 122 - 32)?' (c) (4 points) Find the imaginary part of -2 + iz + 32 + i. 2. (5 points) For this question, let Arg() denote the argument of z lying in [-7, 7). For any > # 0 lying on the circle (e - 1) = 1, show that Arg(2 -1) = 2 Arg(=), and provide a geometric interpretation. Hint: show that cos(Arg(z -1)) = cos(2 Arg(z)) by applying a double angle formula