Here is my second question on the complex numbers assignment. How do I prove the following below?
If z=cos#theta# +isin#theta# , prove that;
1. 1+#z+z^2# =(1+#cos theta)(cos theta+isin theta)#
2. #z//(1+z)=1+itan(theta//2)#
If z=cos
1. 1+
2.
2 Answers
See below
Explanation:
#z= costheta+isintheta#
Factor:
You asked this:
For 1), you are proving that:
#1 + z + z^2 = z(1 + cos theta) qquad equiv qquad 1/z + 1 + z = 1 + cos theta#
Well:
So:
That's not what you're looking for but it is the same as other answer posted here for this question, if you actually finish off the algebra.
For 2) , I think the answer is out by a factor of 2:
Half angle formulae:
Again not the answer you're looking for but I don't see the mistake in the algebra.