# Question c34f3

Aug 31, 2017

i) interpret $1 + \sqrt{2} i$ as coordinates $\left(1 , \sqrt{2}\right)$ and convert to polar coordinates.
First calculate radius r = sqrt(1^2 + sqrt(2)^2 = $\sqrt{3}$

Angle $\theta = {\sin}^{-} 1 \left(\frac{\sqrt{2}}{\sqrt{3}}\right) = 54.74$ degrees (rounding)

...so the polar representation $\left(r , \theta\right) = \left(\sqrt{3} , 54.74\right)$

ii) interpret $1 - \sqrt{2} i$ as coordinates $\left(1 , \sqrt{2}\right)$ and convert to polar coordinates.

radius r = sqrt(1^2 + (-sqrt(2)^2)# = $\sqrt{3}$

Angle $\theta = {\sin}^{-} 1 \left(- \frac{\sqrt{2}}{\sqrt{3}}\right) = - 54.74$ degrees (rounding)
...so polar form is $\left(\sqrt{3} , - 54.74\right)$

iii) when multiplying the polar form of complex numbers, you multiply the magnitude and add the angles.

So, you have $\left({\sqrt{3}}^{2} , \left(54.74 - 54.74\right)\right)$ = (3,0)

iv) I think is incomplete. No idea on this one.