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

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

Answer 2

`z=2(-√(3)+i)`

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((√(3))/(2)+i(1)/(2)`

⇒
`z=2(-√(3)+i)`

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