# Thread: Complex Number, De Moivre and all those kinds of goodies!

1. ## Complex Number, De Moivre and all those kinds of goodies!

Well, this week I have a test on my worst mathematics topic so far. Complex Number. For me, someone who's not that bright, this is simply incomprehensible. I was wondering if someone could explain, in simple language and in digestable way, how to:

• Work with complex numbers and learning to equate them
• Cis form (cos thetha + isin theta) and all that rubbish
• De Moivre's Theorem

All the aid is strongly appreciated!

Please make it simple for me!

~Kindest Regards

2. [quote=JoeyCC;229388]Well, this week I have a test on my worst mathematics topic so far. Complex Number. For me, someone who's not that bright, this is simply incomprehensible. I was wondering if someone could explain, in simple language and in digestable way, how to:

• Work with complex numbers and learning to equate them
I am not too sure what you mean? Could you give an example?

• Cis form (cos thetha + isin theta) and all that rubbish

We define the function $\text{cis}(x)$ to be

$\text{cis}(x)=e^{ix}$

And by Euler's formula we have that $e^{ix}=\cos(x)+i\sin(x)$

So

$\text{cis}(x)=\cos(x)+i\sin(x)$

If you have any specific quetions just ask

• De Moivre's Theorem
This is simply saying

$\left(\cos(x)+i\sin(x)\right)^n=\cos(nx)+i\sin(nx)$

The simple reason is

\begin{aligned}\left(\cos(x)+i\sin(x)\right)^n&=\l eft(e^{ix}\right)^n\\
&=e^{inx}\\
&=\cos(nx)+i\sin(nx)\end{aligned}

Do you have any specific problems or examples we could use to help explain any of these concepts?

3. Firstly, I am having difficulties deducing stuff like:

why $\sqrt3 + i = 2(\sqrt(\dfrac{3}{2}) + \dfrac{1}{2}i)$

and then why $2(\sqrt 3/2 + \dfrac{1}{2}i)$ = 2 cis pi/6

4. Originally Posted by JoeyCC
Well, this week I have a test on my worst mathematics topic so far. Complex Number. For me, someone who's not that bright, this is simply incomprehensible. I was wondering if someone could explain, in simple language and in digestable way, how to:

• Work with complex numbers and learning to equate them
• Cis form (cos thetha + isin theta) and all that rubbish
• De Moivre's Theorem
All the aid is strongly appreciated!

Please make it simple for me!

~Kindest Regards
Sorry, but what you're asking is not reasonable. This material covers several hours worth of class room teaching time.

You should be asking for help as you need it rather than waiting until you have a test and then asking for help on the entire topic. Keep that in mind when you start your next topic.

5. Excuse me sir, but I then asked a specific question:

Originally Posted by JoeyCC
Firstly, I am having difficulties deducing stuff like:

why $\sqrt3 + i = 2(\sqrt(\dfrac{3}{2}) + \dfrac{1}{2}i)$

and then why $2(\sqrt 3/2 + \dfrac{1}{2}i)$ = 2 cis pi/6

6. $2\left(\sqrt{\left(\frac{3}{2}\right)}+\frac{1}{2} i\right)=2\left(\frac{3}{2}\right)^{1/2}+2\frac{1}{2}i=\frac{2\sqrt3}{\sqrt{2}}+i=\sqrt{ 6}+i\ne\sqrt{3}+i$

7. Originally Posted by JoeyCC
Excuse me sir, but I then asked a specific question:
Excuse me, but please treat all users (especially staff members) with respect. Your original post for this thread was very vague and not the type of help we provide. Your second post in this thread is more like it.