- #1
jj364
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Homework Statement
Make a sketch of the complex plane showing a typical pair of complex numbers
z1 and z2
Describe the geometrical figure whose vertices
are z1, z2 and z0 = a + i0.
Homework Equations
z2 − z1 = (z1 − a)ei2π/3
a − z2 = (z2 − z1)i2π/3
where a is a real positive constant.
The Attempt at a Solution
I really am not sure what to do on this question, my initial thoughts were that the solution would look like 3 lines in the complex plane all 2π/3 apart so that it would look like the solution to a roots of unity question.
I tried to rearrange to give z2 in terms of a which yielded
z2(1+e2πi/3 - e2πi/3/(1+e2πi/3) = a(1+e4πi/3/(1+e2πi/3))
But to be honest I really don't know where I am going with this!
Thanks in advance!