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

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

Mathematics
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what 2 things do we need to determine for the trig form?
the absolute value? @amistre64
hmm, i was thinking a radius and an angle
oh sorry, I have no idea how to do this
spose we plot some point (x,y) define as some complex number: x + iy |dw:1440473957824:dw| we can then determine the distance from the origin, and the angle the ray makes with the x axis
r = sqrt(x^2+y^2) a = tan^(-1) (y/x)
okay so I plug the numbers into that formula?
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))
4(cos5pi/6+isin5pi/6)?
?
\[\Large \underbrace{-2}_x+i~\underbrace{2\sqrt3}_y\] \[r=\sqrt{x^2+y^2}=\sqrt{4+12}=4~;~is~fine\] \[\alpha=tan^{-1}(-\frac{1}{\sqrt3})=30^o~(Q2)\]
yeah, looks good to me in my head lol
|dw:1440474530757:dw|
Okay, thank you!
youre welcome

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