Complex Numbers - Modulus, Argument, and Operations on Complex Numbers
Complex Numbers - Modulus, Argument, and Operations on Complex Numbers
The complex number \(z\) has a modulus \(r\) and principal argument \(\theta \) where \(0<\theta <\frac{\pi }{2}\).
Find, in terms of \(r\) and \(\theta \), the modulus and argument of
- \({{z}^{-1}}\)
- \({{z}^{2}}\)
- \(\mathbf{i}z\)
- \(z{{z}^{*}}\)
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Answer: (i) \(\frac{1}{r}\), \(-\theta \) (ii) \({{r}^{2}}\), \(2\theta \) (iii) \(r\), \(\frac{\pi }{2}+\theta \) (iv) \({{r}^{2}}\), \(0\)
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