# 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

#### Answer:

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.