# Thread: Help with Complex Numbers

1. ## Help with Complex Numbers

1.Find the product of and

Are those steps right so far? If so, how do I solve the rest?

2.If and find

But the correct answer is 2+i sq.rt2
How do I get that answer?

2. ## Re: Help with Complex Numbers

Originally Posted by INeedOfHelp
1.Find the product of and

Are those steps right so far? If so, how do I solve the rest?

2.If and find

But the correct answer is 2+i sq.rt2
How do I get that answer?

I find your posting almost impossible to read. Why not learn LaTex?

Given any complex number, it is true $z\cdot\overline{z}=|z|^2$.

3. ## Re: Help with Complex Numbers

Originally Posted by INeedOfHelp
1.Find the product of and

Are those steps right so far? If so, how do I solve the rest?
There are two ways of doing this. The first is essentially what you have done $sin(\pi/6)= \frac{1}{2}$ and $cos(\pi/6)= \frac{\sqrt{3}}{2}$ so that $z= \frac{3\sqrt{3}}{2}+ i\frac{3}{2}$. $\overline{z}= \frac{3\sqrt{3}}{2}- i\frac{3}{2}$. All that has to be multiplied. It is simpler if you realize that $(a+ bi)(a- bi)= a^2+ b^2$, a real number.

The other way is to use the exponential form. saying $z= 3(cos(\pi/6)+ i sin(\pi/6))$ is the same as saying $z= 3e^{i\pi/6}$. And then $\overline{z}= 3e^{-i\pi/6}$. And then the product is $(3)(3)(e^{i\pi/6- i\pi/6})= 9$

2.If and find
$\frac{8e^{\frac{\pi i}{2}}}{4e^{\frac{\pi i}{4}}}= \frac{8}{4}e^{\frac{\pi i}{2}- \frac{\pi i}{4}}= 2e^{\frac{\pi i}{4}}$

And, of course, $2e^{\pi i/4}= 2(cos(\pi/4)+ i sin(\pi/4))$. What is that equal to? (It is NOT "2+ i sq.rt 2"! I suspect you have misread that.)