# How do you express the complex number in rectangular form: z=5(cos 120degrees + i sin 120 degrees)?

Feb 18, 2016

$\left(- \frac{5}{2} , \frac{5}{2} \sqrt{3}\right)$

#### Explanation:

using the formulae that links Polar to Rectangular coordinates.

• x = rcostheta

• y = rsintheta

here r = 5 and $\theta = {120}^{\circ}$

hence :$x = 5 \cos {120}^{\circ} = 5 \times - \frac{1}{2} = - \frac{5}{2}$

and $y = 5 \sin {120}^{\circ} = 5 \times \frac{\sqrt{3}}{2} = \frac{5}{2} \sqrt{3}$