2 In this question you must show detailed reasoning.
The complex numbers \(z _ { 1 }\) and \(z _ { 2 }\) are given by \(z _ { 1 } = 3 - 7 \mathrm { i }\) and \(z _ { 2 } = 2 + 4 \mathrm { i }\).
- Express each of the following as exact numbers in the form \(a + b \mathrm { i }\).
- \(3 z _ { 1 } + 4 z _ { 2 }\)
- \(z _ { 1 } z _ { 2 }\)
- \(\frac { Z _ { 1 } } { Z _ { 2 } }\)
- Write \(z _ { 1 }\) in modulus-argument form giving the modulus in exact form and the argument correct to \(\mathbf { 3 }\) significant figures.