Complex numbers are complexing

There are only two complex arithmetic problems on this set, since you have seen complex numbers before. This one is a little involved, however. You may want to make judicious use of a calculator or a symbol manipulation language like Maple. Of course there is a reason for the fancy real and imaginary parts, and your final expression for http://webwork.mathstat.concordia.ca...84c1362ba1.png will tell you that reason.

I don't have maple but I figured out z=.309016 and then all my other answer where wrong? but if my z=0.309016 can I not just square and cube it and some on?

Re: Complex numbers are complexing

Quote:

Originally Posted by

**M670** There are only two complex arithmetic problems on this set, since you have seen complex numbers before. This one is a little involved, however. You may want to make judicious use of a calculator or a symbol manipulation language like Maple. Of course there is a reason for the fancy real and imaginary parts, and your final expression for

http://webwork.mathstat.concordia.ca...84c1362ba1.png will tell you that reason.

I don't have maple but I figured out z=.309016 and then all my other answer where wrong? but if my z=0.309016 can I not just square and cube it and some on?

How could z possibly be 0.309016? You know that z is complex (and in fact, already have z), what makes you think it is real?

I expect you are supposed to put z into a polar form so you can evaluate $\displaystyle \displaystyle \begin{align*} z^5 \end{align*}$ using DeMoivre's Theorem. From there it might be easier to evaluate the other powers of z.

Re: Complex numbers are complexing

Sorry the real part of Z was 0.309016 but the Imaginary part I didn't get it right

Re: Complex numbers are complexing

Quote:

Originally Posted by

**M670**

This is really interesting question.

You can show that $\displaystyle |z|=1$

Using a computer algebra system, I can see that $\displaystyle z^5=1$.

But I do not know how to do it 'by hand'.

Some way we must show that $\displaystyle \text{Arg}(z)=\left(\frac{2\pi}{5}\right)$. But I have no clue how.

Re: Complex numbers are complexing

Why would they ask such a complicated question ....lol

Re: Complex numbers are complexing

can I not solve it by z=a+bi then (a+bi)(a+bi) to get z^2

Re: Complex numbers are complexing

Does this need to be solved by using De Moivre Theorem ?

Quote:

Originally Posted by

**Plato** This is really interesting question.

You can show that $\displaystyle |z|=1$

Using a computer algebra system, I can see that $\displaystyle z^5=1$.

But I do not know how to do it 'by hand'.

Some way we must show that $\displaystyle \text{Arg}(z)=\left(\frac{2\pi}{5}\right)$. But I have no clue how.

Re: Complex numbers are complexing

Quote:

Originally Posted by

**M670** Does this need to be solved by using De Moivre Theorem ?

Well, the answer to that is clearly yes.

But I have absolutely no idea how to get $\displaystyle \frac{2\pi}{5}$ out of the given.

It is not hard to show that $\displaystyle |z|=1$.