Question

Express the complex number in trigonometric form.
-2

Answer 1

My choices are

2(cos 90° + i sin 90°)
2(cos 0° + i sin 0°)
2(cos 180° + i sin 180°)
2(cos 270° + i sin 270°)

Answer 2

hmm what do you think it is?

Answer 3

Part of your problem is missing? -2 alone is not a complex number ?

Answer 4

That is all that I'm given, solely a -2 @OHgeez

Answer 5

@Ohgeez it is, but the imaginary part of the number is zero

Answer 6

I think it' B @The_Joker<3

Answer 7

well i think your right!

Answer 8

I'm not sure about that actually. Wouldn't it be C because of the negative?

Answer 9

no not c. D

Answer 10

umm.. i actually think its d

Answer 11

why

Answer 12

It is c. Basically its multiplication. You have cos(180) which is -1, and sin(180) which is 0. It leaves you with -2 as the real part, and 0 as the imaginary part

https://www.wolframalpha.com/input/?i=2%28cos+180%C2%B0+%2B+i+sin+180%C2%B0%29

Answer 13

yes i agree with you Train!!

Answer 14

Thanks @LastTrainHome22 Could you help with two more I have?

Answer 15

sure np

Answer 16

umm could i also get a medal ?

Answer 17

Express the complex number in trigonometric form.

3 - 3i

Wouldn't the answer be 3(cos 5pi/4 + i sin 5pi/4) @LastTrainHome22

Answer 18

thanks!!! >:}

Answer 19

???

Answer 20

What you can do for these is graph them on the imaginary plane. Basically the real part of the number represents the horizontal axis while the imaginary part is the vertical axis. In this case you would graph the point (3,-3). Then you find the angle between the line going to that point and the positive horizontal axis. In this case that's 5pi/4. Thats the angle you put behind the sin and cosine. For the coefficient, you basically have to use the pythagorean theorem to find the length of the line from the origin to the point you graphed. In simple terms you square both the real part and the imaginary part, add those numbers together and then take the square root, and that gets you the number you put in front of the expression. So here you have \[\sqrt{3^{2}+3^{2}}\]
which is \[3\sqrt{2}\].

SO the final answer to this one would be [3\sqrt{2}\]\[3\sqrt{2}*[\cos \frac{ 5\pi }{ 4 } + \sin \frac{ 5\pi }{ 4 }]\]