Question

write 6 (cos 330 deg +i sin 330deg in rectagular form

Answer 1

Use eulers formula, and what you know about trigonometric functions

Answer 2

First put it into exponential form

Answer 3

\[re^{i\phi}=r(\cos(\phi)+i\sin(\phi))\]

Answer 4

I assume you want to plot this on an argand diagram? where the imaginary line corresponds to your y axis and the real line corresponds to your horizontal axis

Answer 5

no they dnt want any diagram

Answer 6

Then how do you expect to graph a complex number in the real Cartesian plane

Answer 7

is it -3 sqrt 3+3i

Answer 8

Oh you just want to simplify it in terms of radicals

Answer 9

yeah

Answer 10

I would first change your degrees to radians, and then calculate the cosine and sine functions using memorized values.

Answer 11

alternatively you could just type it on this site, www.wolframalpha.com

Answer 12

It should give you a list of expressions all equivilent

Answer 13

Here il do it for you, and show you what I get

Answer 14

k thanks

Answer 15

thanks

Answer 16

ye

Answer 17

6 (cos 330 deg +i sin 330deg)
Rectangular means a+ ib form...but hey! It does look a bit like it already, so simplify that!
Expand: 6cos330 + 6i sin330
Now cos 330 = cos 30 = sqrt(3)/2(using ASTC rules)
and sin330 = - sin30 = -1/2
So the answer is 6(sqrt(3)/2) + 6i (-1/2) = \[6\sqrt{3}/2 - 3i = 3\sqrt{3} - 3i\]

Answer 18

ohhh i c thanks