Question

Convert the polar representation of this complex number into its rectangular form: z=4(cos150°+ i sin150°) *the i before sin is an imaginary number*

Answer 1

Answer:

$z=2(-\sqrt{3}+i)$

Step-by-step explanation:

The given polar representation of the complex number  is:

$z=4(cos(150)^{\circ}+isin(150)^{\circ})$

Thus, by solving the above equation, we have

⇒$z=4(cos(90+60)+isin(90+60))$

⇒$z=4(-sin60^{\cic}+icos60^{\circ})$

⇒$z=4(\frac{\sqrt{3}}{2}+i\frac{1}{2}$

⇒$z=2(-\sqrt{3}+i)$

which is the required rectangular form of the given polar complex number.

Answer 2

Use z=a+bi=|z|(cos (theta)+i sin(theta)) to find the complex number solutions. z0=z0= -2sqrt3 + 2i