Question

Complex numbers division help please!

Answer 1

If: \[z_1=18cis(-\pi/2), z_2=8cis(\pi/6)\]then how do I find \[z_1/z_2\]?? Thanks heaps!

Answer 2

what's cis ?

Answer 3

cos isin

Answer 4

cos(-pi/2)+i*(-pi/2) = cis(-pi/2)

Answer 5

sorry, i*sin(-pi/2)

Answer 6

is it 9/4 (cis(-2pi/3)) = 9/8(1-isqrt(3))

Answer 7

\[z _{1}=\[18[\cos(-\pi/2)+jsin(-\pi/2)\]
\[z _{2}=8[\cos(\pi/6)+jsin(\pi/6)]\]

Answer 8

You could change it to\[z _{1}=18e ^{-i \pi/2}\]\[z _{2}=8e ^{i \pi/6}\]Then you can use the regular rules for exponential division.

Answer 9

\[z_{1}/z _{2}=r _{1}/r _{2}<\theta _{1}-\theta _{2}\]

Answer 10

I get \[z _{1}/z _{2}=9/4e ^{i \pi(-1/2-1/6)}=9/4e ^{-2i \pi/3}=9/4cis(-2\pi/3)\]

Answer 11

Euler's formular division is better too

Answer 12

Thanks a lot! 9/4cis(-2pi/3) was correct, and with your help I reached this answer myself too!

Answer 13

good q! yw

Answer 14

altho my ans was in polar form, 9/4<(-2*pi/3)