Argand Diagram... S: (1 Viewer)

[ashokkumar]

On an Argand diagram the points P and Q represent the numbers z1 and z2 respectively. OPQ is an equilateral triangle. Show that (z1)^2 + (z2)^2 = z1 x z2

 

[gurmies]

http://community.boredofstudies.org/14/mathematics-extension-2/236297/complex.html

 

[ashokkumar]

is it just me, or do the latex links not load?

 

[khorne]

Yeah they don't load, here's my solution:

p = z1
q = z2 = z1cis60

so z1^2 + z1^2cis120 = z1^2(1+cis120)

RHS z1*z2 = z1^2cis60

but 1+cis120 = cis60

so it's true

 

[ashokkumar]

how come 1 + cis120 = cis60?

 

[Affinity]

how come 1 + cis120 = cis60?

1 + cos(2pi/3) + i*sin(2pi/3) = 1 - 1/2 + i*sqrt(3)/2 = 1/2 + i*sqrt(3)/2 = cos(pi/3) + i*sin(pi/3)