Question

How do you write the complex number in trigonometric form `3-3i`?

Answer 1

In the trigonometric form we will have: `3sqrt(2)(cos(-pi/4)+isin(-pi/4))`

Explanation:

We have
3-3i
Taking out 3 as common we have 3(1-i)
Now multiplying and diving by `sqrt2` we get, 3 `sqrt2`(1/ `sqrt2`- i/ `sqrt2`)

Now we have to find the argument of the given complex number which is tan(1/`sqrt2`/(-1/`sqrt2`)) whixh comes out to be -`pi`/4 .Since the sin part is negative but cos part is positive so it lies in quadrant 4, implying that argument is `-pi/4`.
Hence
`3sqrt(2)(cos(-pi/4)+isin(-pi/4))` is the answer.

Hope it helps!!