Question

Express the complex number in trigonometric form.

4i

Answer 1

trigonometry form : r (cos theta +i sin theta)
so, 3i = 0+3i
now cos part is 0, and the angle which gives cos theta =0 is 90 degrees
= 3 (cos 90 +i sin 90)
thats it!

Answer 2

Thanks for the help, hartnn! But where does the 4 go?

Answer 3

He meant,

trigonometry form : r (cos theta +i sin theta)
so, 4i = 0+4i
now cos part is 0, and the angle which gives cos theta =0 is 90 degrees
= 4 (cos 90 +i sin 90)
thats it!

Answer 4

i solved for 3i
you solve for 4i ^_^

Answer 5

Ohhhh okay thanks guys! is there anyway to give medals to 2 people?

Answer 6

No @kjuchiha , I didn't do anything here. Just give medal to Hartnn ... He deserves it , not I.

Answer 7

btw, @hartnn
instead of taking 90 degree or pi/2 , will it be better to consider principle value for theta?

Answer 8

Alright man thanks guys

Answer 9

give an example with principal value....

Answer 10

Quest. : Express the complex number in trigonometric form.

\(\cfrac{-1}{2} - \cfrac{i\sqrt{3}}{2}\)

r cos theta = -1/2

r sin theta = \(- \cfrac{\sqrt{3}}{2}\)

Therefore, r = 1

Also , tan theta = \(\sqrt{3}\) = \(\tan \cfrac{\pi}{3}\)
Since, \((-1/2 , - \cfrac{\sqrt{3}}{2})\) lies in III quadrant.

Therefore, Principle value of theta is \(-\pi + \cfrac{\pi}{3}\)

Therefore, we get : \(\cos (-\cfrac{2\pi}{3} ) + i \sin ( - \cfrac{2\pi}{3} )\)

Answer 11

Am I wrong somewhere, @hartnn ? Or is it right?

Answer 12

i think its correct...in this case(4i) principle value = 90, right ?