Let R+ denote the multiplicative group of positive real
Chapter 8, Problem 13SE(choose chapter or problem)
Let \(\mathbf{R}^{+}\) denote the multiplicative group of positive real numbers and let \(T=\left\{a+b i \in \mathbf{C}^* \mid a^2+b^2=1\right\}\) be the multiplicative group of complex numbers on the unit circle. Show that every element of \(\mathbf{C}^*\) can be uniquely expressed in the form rz, where \(r \in \mathbf{R}^{+}\) and \(z \in T\).
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