# Thread: Complex Numbers, Polar Coordinates

1. ## Complex Numbers, Polar Coordinates

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?

2. Originally Posted by jschlarb
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?
Please show >all< of your working ..... Then it will be much easier to explain your mistakes to you ....

3. 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?)

4. Originally Posted by jschlarb
z= -1+7i or polar coordinates
First just do the basic computations: $\displaystyle \theta = \arg \left( { - 1 + 7i} \right) = \arctan \left( {\frac{7}{{ - 1}}} \right) + \pi \,\& \,\sqrt {\left( { - 1} \right)^2 + 7^2 } = 5\sqrt 2$.
Now $\displaystyle z = 5\sqrt 2 e^{i\theta }$.

5. Originally Posted by jschlarb
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 $\displaystyle z = -1 + 7i = r (\cos \theta + i \sin \theta) = .....$