smc-1191-40-Multiplication

The complex numbers \(z=2 e^{i\small{\dfrac{\pi}{2}}}\) and \(w=6 e^{i \small{\dfrac{\pi}{6}}}\) are given.

Find the value of \(zw\) , giving the answer in the for \(r e^{i \theta}\). (2 marks)

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\(12 e^{i 2 \small{\dfrac{\pi}{3}}}\)

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\(zw\)	\(=2 e^{i \small{\dfrac{\pi}{2}}} \cdot 6 e^{i \small{\dfrac{\pi}{6}}}\)
	\(=12 e^{i \small{\dfrac{\pi}{2}}+i \small{\dfrac{\pi}{6}}}\)
	\(=12 e^{i \small{\dfrac{2 \pi}{3}}}\)