# Polar and Rectangular forms

• Jan 17th 2008, 04:49 PM
OzzMan
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.
• Jan 17th 2008, 05:03 PM
Jhevon
Quote:

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)
• Jan 17th 2008, 10:19 PM
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? And btw I'm not exactly sure by what you mean multiply it out. You want me to multiply the polar form out?
• Jan 17th 2008, 10:33 PM
Jhevon
Quote:

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.

Quote:

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
• Jan 17th 2008, 10:53 PM
OzzMan
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.
• Jan 17th 2008, 10:54 PM
OzzMan
nevermind i know what i did wrong. thanks for the help.