ashokkumar
Mr
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
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Argand Diagram... S: (1 Viewer)
- Thread starter ashokkumar
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gurmies
Drover
ashokkumar
Mr
is it just me, or do the latex links not load?
K
khorne
Guest
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
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
Mr
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)