Question

TRIGONOMETRY:

Write z = the square root of 3 minus i. in abbreviated trigonometric form.

Answer 1

fist find the magnitude?

Answer 2

\[Z=x+i y\]
\[|Z|=\sqrt{x^2+y^2}\]

Answer 3

So I just plug in y as -1 and x as root(3)? That's all there is to it?

Answer 4

yes @dumbsearch2

Answer 5

Then what?

Answer 6

\[\Theta=\tan^{-1}(\frac{ y }{ x }) =\]\[\Theta=\tan^{-1}(\frac{ -1 }{ \sqrt{3} })=-30^0\]
in fourth quarter

Answer 7

What is that?

Answer 8

I did:

|Z| = root((root(3))^2+(-1)^2)

and I found:

|Z| = 2.

What now?

Answer 9

complex number: magnitude + angle

Answer 10

How should I proceed? I found that |Z| = 2.

Answer 11

this the magnitude, and now we should find the angle

Answer 12

\[\Theta=\tan^{-1}(\frac{ y }{ x }) =\]\[\tan^{-1}(\frac{ -1 }{ \sqrt{3} })=-30^0\]

Answer 13

\[Z=x+iy=re^{i \theta}=r(\cos \theta+isin \theta)\]=\[rCis\]
and\[r=|Z|\]

Answer 14

r=|Z|=2

Answer 15

\[\theta=-30^0=330^0\]

Answer 16

Plug values of r & θ in: (rCis θ)

Answer 17

Thank you so much! Most importantly, I know how to do the problem by myself now, in the clear manner in which you explained it... thanks a million!

Answer 18

@dumbsearch2 no problem, you are welcome in any time.

Answer 19

I want to do the same thing for the next problem:

"Write z = -5 in abbreviated trigonometric form."

However, why isn't there an i? Also how can I find the x and the y for the magnitude if there is only one variable (-5)?

Answer 20

I finished complex course since 1 year only. it is interesting.

Answer 21

Z=-5+i0

Answer 22

x=-5, y=0

Answer 23

Thank you!

Answer 24

|Z| = 5, right?

Answer 25

not 0