Question

Find the quotient of 6(cos(11pi/6) + i sin(11pi/6) divided by ((cos3pi/2) + i sin (3pi/2))


The quotient is 3 + i 3 sqroot(3).?

Answer 1

\[\frac{6(\cos(11\pi/6) + i \sin(11\pi/6)}{(\cos3\pi/2) + i \sin (3\pi/2)} \cdot \frac{(\cos3\pi/2) - i \sin (3\pi/2)}{(\cos3\pi/2) - i \sin (3\pi/2)}\]

Answer 2

This is the tricky way, convert it into polar form, and convert it back into rectangular after division.

\[r(\cos(x)+isin(x))=r(e^{ix})\]

Answer 3

\[6(\cos(11 \pi/6)+isin(11 \pi/6))=6e^{i(11\pi/6)}\]
\[(\cos(3 \pi/2)+isin(3 \pi/2))=e^{i(3\pi/2)}\]

Answer 4

And use\[\frac{a^m}{a^n}=a^{m-n}\]

Answer 5

So division now turns into subtraction- much less messy!