Question

I) Express Z1 in polar Form
a) Z1=1-(2-√3)i (complex number)

Answer 1

`z_1=1-(2-√(3))i=2\sqrt{2-√(3)}[cos((23\pi)/(12) )+isin((23\pi)/(12) )]`

Explanation:

Recall that
`a+bi=r(cos\theta+isin\theta)` where
`r=√(a^2+b^2)` and
`\theta=tan^(-1)((b)/(a))`.

Since
`a=1` and
`b=-2+√(3)`, then
`r=\sqrt{(1)^2+(-2+√(3))^2}=2\sqrt{2-√(3)}` and
`\theta=tan^(-1)((-2+√(3))/(1))=-(\pi)/(12)=(23\pi)/(12)`.

Therefore,
`z_1=1-(2-√(3))i=2\sqrt{2-√(3)}[cos((23\pi)/(12) )+isin((23\pi)/(12) )]`

Answer 2

Explanation:

hope it will help you thank you