Polar Form

**Mathsnewbie** · November 3rd 2008, 08:53 AM

Hey guys wondered if someone could help me out again, if you let Z=root 3 - i what is Z in polar form?

Then how do I find the real and imaginary parts of (z^7)/8?

**HallsofIvy** · November 3rd 2008, 10:04 AM

Originally Posted by Mathsnewbie

Hey guys wondered if someone could help me out again, if you let Z=root 3 - i what is Z in polar form?

Then how do I find the real and imaginary parts of (z^7)/8?

$x= r cos(\theta)$ and $y= r sin(\theta)$ so [tex]x^2+ y^2= r^2 cos^2(\theta)+ r^2 sin^2(\theta)= r^2[/itex]: $r= \sqrt{x^2+ y^2}$ . Dividing y by x, $y/x= sin(\theta)/cos(\theta)= tan(\theta)$ and [tex]\theta= arctan(y/x)[/itex].
Here, $x^2+ y^2= 3+ 1= 4$ so r= 2. [tex]y/x= -1/\sqrt{3}[tex] so [tex]tan(\theta)= -1/\sqrt{3}[/itex] and $\theta= -\pi/6$ .

Once you have Z in polar form, $Z^8$ has $r= 2^8= 256$ and [tex]\theta= 8(-\pi/6)= -4\pi/3[/itex]. The real part of $Z^8$ is $256 cos(4\pi/3)$ and the imaginary part is $- 256 sin(4\pi/3)$ .

Thread: Polar Form

LinkBack

Thread Tools

Display

Polar Form

Similar Math Help Forum Discussions

Polar form

Rectangular form into Polar Form

Converting from Polar form to Rectangular form

polar form

From polar form to rectangular form..help!

Search Tags