Question

What is the trigonometric form of `(4-4i)`?

Answer 1

`=4sqrt2[cos(-(3pi)/4)+isin(-(3pi)/4)]`

Explanation:

The trigonometric form looks like this : `r(costheta+isintheta)`

where `r` is the modulus and `theta` the arguement.

Step 1:
find the modulus(magnitude)
`r=sqrt((4)^2+(-4)^2)=4sqrt(2)`

Step 2:
find the arguement.
`theta= arctan(4/4)- pi= pi/4-pi=-(3pi)/4`

Step 3:
`z=4sqrt2[cos(-(3pi)/4)+isin(-(3pi)/4)]`