Question

Question #c34f3

Answer 1

i) interpret `1 + sqrt(2)i` as coordinates `(1,sqrt(2))` and convert to polar coordinates.
First calculate radius `r = sqrt(1^2 + sqrt(2)^2` = `sqrt(3)`

Angle `theta = sin^-1(sqrt(2)/sqrt(3)) = 54.74` degrees (rounding)

...so the polar representation `(r,theta) = (sqrt(3), 54.74)`

ii) interpret `1 - sqrt(2)i` as coordinates `(1, sqrt(2))` and convert to polar coordinates.

radius `r = sqrt(1^2 + (-sqrt(2)^2)` = `sqrt(3)`

Angle `theta = sin^-1(-sqrt(2)/sqrt(3)) = -54.74` degrees (rounding)
...so polar form is `(sqrt(3), -54.74)`

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

So, you have `(sqrt(3)^2 , (54.74 - 54.74))` = (3,0)

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