Question

Express the complex number in trigonometric form. -2i

Answer 1

you need two numbers \(r\) and \(\theta\)
\[r=|2i|\] which should be pretty obvious
what do you get ?

Answer 2

2(cos(3Pi/2)+i sin(3Pi/2))------> expand and get the answer

Answer 3

if it is not clear let me know but if you guess you will no doubt be right

Answer 4

@satellite73 Do you mean i as in an imaginary number..? I have to use this for vectors and the demoivre theorem so wouldn't the "i" stand as an "i" in a vector?

Answer 5

hold the phone
lets go slow

Answer 6

\(i\) in this case is the "imaginary unit" meaning \(i=\sqrt{-1}\) or \(i^2=-1\)

Answer 7

the number \(-2i\) lives in the complex plane
it is here

Answer 8

to write in trig form as
\[-2i=r\left(\cos(\theta)+i\sin(\theta)\right)\] you need two numbers, \(r\) and \(\theta\)

Answer 9

\(r\) is the absolute value
the distance from zero
what is that number?

Answer 10

2? in this case?

Answer 11

yes

Answer 12

in general the absolute value of \(a+bi\) is \(\sqrt{a^2+b^2}\) but in this case it is completely obvious that is is \(2\)

Answer 13

now you need \(\theta\)

Answer 14

that angle
what is it?

Answer 15

3pi/2

Answer 16

yes

Answer 17

it is also \(-\frac{\pi}{2}\) and an infinite number of other angles, it is not unique, but \(\frac{3\pi}{2}\) will work

Answer 18

that means
\[-2i=2\left (\cos(\frac{3\pi}{2})+i\sin(\frac{3\pi}{2})\right)\][

Answer 19

ohhhh... now I get it :):) thank you so muuchh

Answer 20

yw

Answer 21

@satellite73 sorry but if it were to be 6-6i what would happen? since it's getting subtracted from 6?