Question

Find modulus and principle argument of compiles numbers Z=5/2(cos300+isin300)

Answer 1

$z = \frac{5}{2}(\cos(300) + i\sin(300)) = \frac{5}{2}(\frac{1}{2} - i\frac{\sqrt{3}}{2})\\|z| = \sqrt{(\frac{5}{4})^2 + (\frac{5\sqrt{3}}{4})^2} = \sqrt{\frac{25}{16} + \frac{75}{16}} = \sqrt{\frac{100}{16}} = \frac{10}{4} = \frac{5}{2}$