Conjugates, division and equating parts Problem set A Answers

1. (a) \(z^* = 4 + 9i\)
2. (b) \(zz^* = 100\)
3. (c) \(z^* = -7 - 2i,\ zz^* = 53\)

1. (a) \(2x\), real
2. (b) \(2(x^2 - y^2)\), real

1. (a) \(4 + 2i\)
2. (b) \(\frac{18}{5} - \frac{1}{5}i\)
3. (c) \(\frac{2}{13} + \frac{3}{13}i\)

1. (a) \(z = 3 + 4i\)
2. (b) \(z = -3 + 2i\)

1. (a) \(a = 3,\ b = -2\)
2. (b) \(a = 1,\ b = 3\)

1. (a) \(7 - i\) amps
2. (b) \(ZZ^* = 20\) ohms squared

\(z = 2 + i\)

1. (a) \(zz^* = 5,\ z + z^* = 2\)
2. (b) \(\frac{2}{5}\)