Question

convert z=(-5 sqrt 3)/2+(5/2)i and w=1+(sqrt3)i to polar form

Answer 1

HI!!

Answer 2

learned that from @misty1212

Answer 3

you need two numbers to write
\[-\frac{5\sqrt3}{2}+\frac{5}{2}i\] in polar form
\[r\left(\cos(\theta)+i\sin(\theta)\right)\] namely \(r\) and \(\theta\)

Answer 4

\(r\) is the easiest
it is
\[r=\sqrt{a^2+b^2}\] which in your case is
\[r=\sqrt{(\frac{5\sqrt3}{2})^2+(\frac{5}{2})^2}\] let me know what you get

Answer 5

I get 5

Answer 6

yeah me too

Answer 7

now you need \(\theta\)
\[\cos(\theta)=\frac{a}{r}\] which in your case is conveniently
\[-\frac{\sqrt3}{2}\]

Answer 8

i got -8.66

Answer 9

also
\[\sin(\theta)=\frac{b}{r}=\frac{1}{2}\] find an angle \(\theta\) with
\[\cos(\theta)=-\frac{\sqrt3}{2}\] and
\[\sin(\theta)=\frac{1}{2}\]

Answer 10

use radians, not decimals

Answer 11

don't know how to do that

Answer 12

it is a really really familiar point on the unit circle
\[\left(-\frac{\sqrt3}{2},\frac{1}{2}\right)\]

Answer 13

you got a unit circle cheat sheet?

Answer 14

now you do

Answer 15

5pi/6

Answer 16

bingo

Answer 17

polar form
\[5\left(\cos(\frac{5\pi}{6})+i\sin(\frac{5\pi}{6})\right)\]

Answer 18

what about w=1+(sqrt 3)i

Answer 19

repeat the process above
\[r=\sqrt{a^2+b^2}\] and
\[\cos(\theta)=\frac{a}{r}\\
\sin(\theta)=\frac{b}{r}\] finds you \(r\) and \(\theta\)

Answer 20

r=2

Answer 21

theta=60 degrees

Answer 22

yes!

Answer 23

so what would the polar form be

Answer 24

use radians not degrees

Answer 25

what is 60 in radians

Answer 26

1.04

Answer 27

polar
\[w=2(\cos \theta+i\sin \theta) \]
\[\theta =60 ~~degree \]

Answer 28

no no decimal my friend see what satellite did with the first
use radians

Answer 29

don't know who to do

Answer 30

see the cheat sheet

Answer 31

pi/3

Answer 32

yes