Question

BEST RESPONSE
Express the complex number in trigonometric form.

-3i

Answer 1

-3(cos 90+i sin 90)

Answer 2

are you sure?

Answer 3

yep :) where 90 is in degrees

Answer 4

I don't have a negative 3 answer choice though, so would it be the same only with a positive 3?

Answer 5

is this a test ?

Answer 6

no its just a homework assignment

Answer 7

ok then u can wrote it also as

3(cos 90- i sin 90)

Answer 8

Thank you! Can you help me with one more similar one?

Answer 9

No, that won't do... you can't have cos A - isin A

Answer 10

3(cos 90- i sin 90)=-3 sin 90

Answer 11

Unless it's in the choices, of course, I'd concede :)

Answer 12

*-3i sin 90

Answer 13

It has to be cos A + i sin A
never a difference.

It's more like
3(cos 270 + i sin 270)

Answer 14

so which one is it?

Answer 15

@AravindG
What do you think? :>

Answer 16

ya u r right :)

Answer 17

Yay, I convinced @AravindG
Better add that to my list of achievements

LOL anyway, yeah, that's it :)

Answer 18

You had another question @danny369 ?

Answer 19

Yes, Express the complex number in trigonometric form.

-3 + 3 squareoot (3) i

Answer 20

I knew this had to happen sometime :D
First, acquaint yourself with the complex plane :D
For a complex number a + bi

Answer 21

So which is it?

Answer 22

the box that is 90- 180 degrees

Answer 23

right :)
So, to get the polar form
r(cos A + i sin A)
You need r, and you need A :D
getting r is relatively straightforward, use this formula
\[\large r = \sqrt{a^2 + b^2}\]

Answer 24

just to add in here :

\[-\pi < \theta \le \pi \] is often used to repesent \(\theta \) as principal argument

Answer 25

okay so r would be 4.4426?

Answer 26

i mean 4.2426

Answer 27

Try it again
\[\large a = 3 \ \ ; \ \ b=3\sqrt3\]

Answer 28

ohh so its 6

Answer 29

Yep. Now finding the angle A is a bit tricky, first you might want to evaluate this
\[\large A = \tan^{-1}\frac{b}{a}\]

Answer 30

is it 60?

Answer 31

Well, almost. But remember, you picked the quadrant where the angle is from 90 - 180. So what's it gonna be? :)

Answer 32

Okay, in general, this is going to be a mouthful, but it's accurate, trust me :)
given the complex number a + bi
Use these rules
If a and b are both positive, then\[\large A = \tan^{-1}\left|\frac{b}{a}\right|\]
If a is negative and b is positive\[\large A = 180^o -\tan^{-1}\left|\frac{b}{a}\right|\]
If both a and b are negative\[\large A = 180^o +\tan^{-1}\left|\frac{b}{a}\right|\]
If a is positive and b is negative \[\large A = 360^o -\tan^{-1}\left|\frac{b}{a}\right|\]

Answer 33

Im confused

Answer 34

Well, as you pointed out, a is negative and b is positive, right?

Answer 35

yes

Answer 36

So, you got 60 for the angle right? But a is negative and b is positive, if you consult that mouthful of rules I gave you, you'll find that the angle A is equal to
180 - 60 = 120

Get it now? :)

Answer 37

oh okay, yes I understand
what do we do next?

Answer 38

that's it :)
r = 6
A = 120
So just plug in
\[\large r\left(\cos A + i\sin A\right)\]

Answer 39

Got it yet?

Answer 40

I understand, but the answers come in the form of pi

Answer 41

oh, sorry.
First, let me revise in terms of pi
Given the complex number a + bi
If a and b are BOTH POSITIVE\[\large A = \tan^{-1}\left|\frac{b}{a}\right|\]
If a is negative and b is positive\[\large A =\pi -\tan^{-1}\left|\frac{b}{a}\right|\]
If a and b are BOTH NEGATIVE\[\large A = \pi+\tan^{-1}\left|\frac{b}{a}\right|\]
If a is positive and b is negative \[\large A = 2\pi -\tan^{-1}\left|\frac{b}{a}\right|\]

Answer 42

would it be 2pi/3?

Answer 43

One more thing. If you have the angle measure in degrees, you just multiply it by
\[\large \frac{\pi}{180}\]
To get it in radians.

And you're correct, by the way, so what's your final answer?

Answer 44

6 ( cos 2pi/3 + i sin 2pi/3)!
Thank you so much!

Answer 45

No problem :)

Answer 46

Going off now
------
Terence out
;)