Answer:
Option d is correct that is [tex]z=\sqrt{18} cos(\frac{7\pi}{4})+i sin(\frac{7\pi}{4})[/tex]
Step-by-step explanation:
We have been given a complex number 3-3i we have to convert it in the polar form:
polar form of a complex number:
[tex]z=r(cos{\theta}+i sin{\theta})[/tex]
Where, [tex]r=\sqrt{x^2+y^2}[/tex]
the general form of complex number is:
x+iy
Here, x=3 and y=-3
Hence, [tex]r=\sqrt{3^2+(-3)^2}=\sqrt{18}[/tex]
And [tex]\theta=tan^{-1}\frac{y}{x}[/tex]
[tex]\theta=tan^{-1}\frac{-3}{3}[/tex]
[tex]\Rightarrow \theta=tan^{-1}(-1)[/tex]
[tex]\Rightarrow \theta=2{\pi}-\frac{\pi}{4}[/tex]
[tex]\Rightarrow \theta=\frac{7\pi}{4}[/tex]
Hence, substituting all the values in polar form formula we get:
[tex]z=\sqrt{18} cos(\frac{7\pi}{4})+i sin(\frac{7\pi}{4})[/tex]
Therefore, option d is correct.
