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

Question

8065 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-15T10:21:47

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

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

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