Express the complex number in trigonometric form.

-2 + 2square root of threei

Question

Express the complex number in trigonometric form. 

-2 + 2square root of threei

anonymous · Answer

@mathmath333

anonymous · Answer

@dan815

anonymous · Answer

SOMEONE HELP

amistre64 · Answer

what 2 things do we need to determine for the trig form?

anonymous · Answer

the absolute value? @amistre64

amistre64 · Answer

hmm, i was thinking a radius and an angle

anonymous · Answer

oh sorry, I have no idea how to do this

amistre64 · Answer

spose we plot some point (x,y) define as some complex number: x + iy

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we can then determine the distance from the origin, and the angle the ray makes with the x axis

amistre64 · Answer

r = sqrt(x^2+y^2)

a = tan^(-1) (y/x)

anonymous · Answer

okay so I plug the numbers into that formula?

amistre64 · Answer

what else would you do with a formula?

trig defines x = r cos(a) and y=r sin(a)

therefore our trig form of a complex number is:

x + iy  to  r cos(a) + r i sin(a)

or simplified to:  r (cos(a) + i sin(a))

anonymous · Answer

4(cos5pi/6+isin5pi/6)?

anonymous · Answer

?

amistre64 · Answer

$$\Large \underbrace{-2}_x+i~\underbrace{2\sqrt3}_y$$
$$r=\sqrt{x^2+y^2}=\sqrt{4+12}=4~;~is~fine$$
$$\alpha=tan^{-1}(-\frac{1}{\sqrt3})=30^o~(Q2)$$

amistre64 · Answer

yeah, looks good to me in my head lol

amistre64 · Answer

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