Question

Express each complex number in polar form:
-4+i

Answer 1

21

Answer 2

lol @bv54654

Answer 3

but seriously I need help getting theta

Answer 4

Note that complex numbers are in the form \[z=a+ib\] so to convert it into polar forms where \[a = rcos \theta~~~\text{and}~~~b=r \sin \theta\] where \[r^2=a^2+b^2\] also note \[r = |z| \implies z=|z|(\cos \theta + i \sin \theta)\]

Answer 5

you'll also use
\[\Large \theta = \arctan\left(\frac{b}{a}\right)\]

Answer 6

Haha yes, I was about to just put that

Answer 7

keep in mind that you'll end up in Q2

using arctan will land you in Q4, so you'll need to add on 180 degrees or pi radians to whatever arctan results in

Answer 8

how do you know in which quadrant it ends up in and how much do you add for the specific quadrant??

Answer 9

the range of arctan is -90 < theta < 90 which covers Q1 and Q4

if the input of arctan is negative, then you end up in Q4. If positive, then you end up in Q1

Answer 10

`how much do you add for the specific quadrant??` you add on 180 degrees to make a half rotation


example: say that the result of arctan was -30 degrees. Add on 180 to get 180+(-30) = 150 degrees

Answer 11

Ok,so for theta I got 165.96, but for some reason my text book writes it down in the answer as 2.90 I have no idea what is going on

Answer 12

the answer they wrote is in radian form

convert 165.96 degrees to radians by multiplying by the conversion factor (pi/180)

165.96*(pi/180) = 2.89661399046292

which rounds to 2.90 radians

Answer 13

the better route is probably just to change your calculator to radian mode

Answer 14

Oh ok, so should I have it changed from the beginning?

Answer 15

no you can be in degree mode and convert at the end like I did above. Either way works

Answer 16

Oh ok I appreciate your help Thank You @jim_thompson5910 and @Astrophysics

Answer 17

no problem