Okay, I have this so far
z= -1+7i
As far as what I have for polar coordinate equation, this is it:
z= 6.93(cos180+ i sin?)
My problem is that 7 cannot be converted into an angle.
What would I do for this?
z=-1+7i
a=-1, b=7, r= $\displaystyle [square root] a^2+b^2$ = 6.93 (subbed in -1 and 7)
$\displaystyle cos^-1 (-1) = 180, sin^-1 (7) = does not exist$
z=6.93(cos180+ i sin ?)
You'll have to forgive me, I'm not sure of the tag for square roots (if there is a link to all math signs, could you please link it?)
You should know that the argument of z = a + ib is $\displaystyle \theta = \tan^{-1} \frac{b}{a}$ where you have to be careful what quadrant (and hence value) you choose for $\displaystyle \theta$ ..... A simple argand diagram showing z = a + ib will help you make that decision.
For the question you've posted, $\displaystyle \theta = \tan^{-1} \frac{7}{-1} = \tan^{-1} (-7)$.
An argand diagram easily shows that z = -1 + 7i lies in the 2nd quadrant, so $\displaystyle \theta = \tan^{-1} (-7) + \pi \approx -1.429 + \pi = 1.713$ radians.
Therefore $\displaystyle z = -1 + 7i = r (\cos \theta + i \sin \theta) = .....$