Trigonometry
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Given z1=5(cosπ6+isinπ6)z_1=5\left(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6}\right) and z2=3(cos3π4+isin3π4)z_2=3\left(\cos\frac{3\pi}{4}+i\sin\frac{3\pi}{4}\right), find the product z1・z2z_1・z_2.
z1・z2=15CiS(11π212)z_1・z_2=15CiS\left(\frac{11\pi^2}{12}\right)
z1・z2=15CiS(π2)z_1・z_2=15CiS\left(\frac{\pi}{2}\right)
z1・z2=CiS(π22)z_1・z_2=CiS\left(\frac{\pi^2}{2}\right)
z1・z2=15CiS(11π12)z_1・z_2=15CiS\left(\frac{11\pi}{12}\right)