# How do you write 2(cos300+isin300) in retangular form?

Feb 3, 2015

The answer is: $z = 1 - \sqrt{3} i$.

The rectangular form of a complex number is:

$z = a + i b$,

and we have a number written in trigonometric form, that is:

$z = \rho \left(\sin \theta + i \cos \theta\right)$.

So the real part of the numer is rhosintheta=2cos300°=2*1/2=1 and the imaginary part is 2sin300°=2*(-sqrt3/2)=-sqrt3#.

So:

$z = 1 - \sqrt{3} i$.