complex help!!!!! (1 Viewer)

[nealos]

Hey
Could some1 help me with this Q from Patel..

P represents a point on the argand plane, if it is rotated 30*, and 45 * find the new complex number of the rotated point..

I was confused in how to start it and the methods used..
Any help will be ood
thanks

 

[Wackedupwacko]

let P = x+iy

rotated by 30degrees means P(cis Pi/6)
expanding = xcos pi/6 - y sin pi/6 + i(xsin pi/6 + ycos pi/6)

= x sqrt3/2 -y/2 +i (x/2 + y sqrt 3 /2)

also since u can rotate clockwise instead of anti clockwise just replace the angle as -pi/6 instead of pi/6 which becaomse

= xcos -pi/6 -ysin -pi/6 +i (xsin -pi/6 + ycos -pi/6)
= x sqrt3 /2 + y/2 +i (-x/2 + y sqrt3/2)

use similar method of 45 degrees except replace pi/6 with pi/4

ie

Pcis pi/4 or Pcis -pi/4

= [x-y + i(x+y)]/sqrt 2

or

= [x+y+i(y-x)]/sqrt 2

 

[nealos]

thanks heaps