We need to find r and θ.

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

`= sqrt(7^2 +(-5)^2)`

`= sqrt(49+25)`

`= sqrt(74) ~~8.6`

To find θ, we first find the acute angle α (see Trigonometric Functions of Any Angle if you are rusty on this):

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

`= tan^(-1)(5/7)`

`~~35.54^text(o)`

Now, `7 - 5j` is in the fourth quadrant, so

`θ = 360^@ - 35.54^@ = 324.46^@`

So, expressing `7 - 5j` in polar form, we have:

`7 - 5j ` `= 8.6 (cos\ 324.5^@ + j\ sin\ 324.5^@)`

We could also write this answer as `7 - 5j = 8.6\ "cis"\ 324.5^@`.

Also we could write: `7 - 5j = 8.6 ∠ 324.5^@`

The graph is as follows:

Representing a complex number using polar coordinates

Easy to understand math videos:
MathTutorDVD.com