Question

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

Answer 1

Step-by-step explanation:

hope it will help you thank you

Answer 2

Answer:

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

Step-by-step explanation:

Recall that $a+bi=r(cos\theta+isin\theta)$ where $r=\sqrt{a^2+b^2}$ and $\theta=tan^{-1}(\frac{b}{a})$.

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

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