Question

Express the complex number in trigonometric form.

-6 + 6 sq3 i

Answer 1

\(-6(1 - i\sqrt{3}) = -3\left(\dfrac{1}{2} - i\dfrac{\sqrt{3}}{2}\right)\)

That's a beautiful thing. Just where is that angle?

Answer 2

Every complex number can be represented in the form: \[r e^{i \theta}\]
See the attached diagram.
dw:1391931141989:dw|

Hence in this case: r=sqrt(36x4)=12 and tan(theta)=sqrt(3) giving theta=(pi/3)
Thus we can write the number as:

\[12 e ^{\pi/3}\]

Which using Euler's Identity can be expressed as:

\[12 [\cos(\pi/3)+i \sin(\pi/3)]\]

Answer 3

Wow?! So WHERE did I get 3? 6*2 = 12. Oh, will you look at that!! Time to go to bed, I think.