Complex number on plane

`r=sqrt(x^2+y^2)`

`= sqrt( (sqrt(2))^2 +(sqrt(2))^2)`

`= sqrt(2+2)`

`= sqrt(4)`

` =2`

To find `θ`, we first find the acute angle `alpha`:

`alpha = tan^(-1)(y/x)`

`=tan^(-1)(sqrt(2)/(sqrt(2)))`

` ~~ 45^text(o)`

The complex number is in the 4th quadrant, so

`θ = 360^@ - 45^@ = 315^@`

So we can write:

`sqrt2 - jsqrt2 = 2\ ∠\ 315^@`

` = 2(cos315^@ + jsin315^@)`