# Thread: Polar and Rectangular forms

1. ## Polar and Rectangular forms

I need to put 3e^(.5i) in rectangular and polar forms. i being imaginary number and .5 being in radians. When i convert .5 radians into degrees i get 28.6 degrees. When i do the math i get 3(cos28.6 + i*sin28.6) for the polar form. But i have no idea how to get the rectangular form from here. Pretty much working backwards.

2. Originally Posted by OzzMan
I need to put 3e^(.5i) in rectangular and polar forms. i being imaginary number and .5 being in radians. When i convert .5 radians into degrees i get 28.6 degrees. When i do the math i get 3(cos28.6 + i*sin28.6) for the polar form. But i have no idea how to get the rectangular form from here. Pretty much working backwards.
just multiply out and evaluate the trig functions, then you would get it in a + ib form

if you wanted to work hard you could realize that to go from $re^{i \theta} \to x + iy$:

$r = \sqrt{x^2 + y^2}$ and $\theta = \arctan \frac yx$

(and don't convert to degrees)

3. If I'm doing a question similar to this except i have to put it in exponent form and i end up with something like 5e^(38.9 degrees*i) should i always convert the degrees to radians in this? And btw I'm not exactly sure by what you mean multiply it out. You want me to multiply the polar form out?

4. Originally Posted by OzzMan
If I'm doing a question similar to this except i have to put it in exponent form and i end up with something like 5e^(38.9 degrees*i) should i always convert the degrees to radians in this?
you shouldn't be ending up in degrees to begin with. work in radians unless you are specifically told otherwise.

And btw I'm not exactly sure by what you mean multiply it out. You want me to multiply the polar form out?
yes, expand the brackets, then simplify

5. when i multiply it all out i get 4.07. I used .5 instead of 28.6 degrees in the multiplication also. the books answer is 2.63 + 1.44i . i'm still confused. sorry.

6. nevermind i know what i did wrong. thanks for the help.