1. ## De Moivre's Theorem and quadratics

a) Find all solutions of the equation. (Write your answers in the form a + bi. Enter your answers as a comma-separated list.)

Answers I got for this is -2 + 2i and -2-2i..I assume you just use the quadratic formula and solve..is that right?

b) Find the indicated power using De Moivre's Theorem.

Don't know if I did it right, but I got 1024i for this problem..can someone verify?

2. Originally Posted by Jgirl689
a) Find all solutions of the equation. (Write your answers in the form a + bi. Enter your answers as a comma-separated list.)

Answers I got for this is -2 + 2i and -2-2i..I assume you just use the quadratic formula and solve..is that right?

b) Find the indicated power using De Moivre's Theorem.

Don't know if I did it right, but I got 1024i for this problem..can someone verify?
Code:
>> syms x;
>> solve('x^2 + 2*x + 5 = 0',x)

ans =

- 2*i - 1
2*i - 1
Code:
>> (1+ sqrt(-1))^20

ans =

-1024

3. [quote=Jgirl689;506170]a) Find all solutions of the equation. (Write your answers in the form a + bi. Enter your answers as a comma-separated list.)

Answers I got for this is -2 + 2i and -2-2i..I assume you just use the quadratic formula and solve..is that right?

yes, it is

b) Find the indicated power using De Moivre's Theorem.

Don't know if I did it right, but I got 1024i for this problem..can someone verify?

check again!!!!

4. Originally Posted by rubic
b) Find the indicated power using De Moivre's Theorem. Don't know if I did it right, but I got 1024i for this problem..
Not right, but close.

$\displaystyle \left(1+i\right)^{20} = \left\{\sqrt{2}\left[\cos\left(\dfrac{\pi}{4}\right)+i\sin\left(\dfrac{ \pi}{4}\right)\right]\right\}^{20}$ $\displaystyle = \left(\sqrt{2}\right)^{20}\left\{\cos\left(\dfrac{ 20\pi}{4}\right)+i\sin\left(\dfrac{20\pi}{4}\right )\right\}$ $\displaystyle = 2^{10}\bigg\{\left(5\pi\right)+i\sin\left(5\pi\rig ht)\bigg\}$ $\displaystyle = 2^{10}\bigg\{\cos\left(\pi\right)+i\sin\left(\pi\r ight)\bigg\} = 2^{10}\left(-1+i(0)\right) = -2^{10}.$

5. ## Please help me to find out,A problem on De Moivres theorem

First i apologize if i have posted at wrong place....

The problem is here:

Solve x^8+x^5+x^3+1 by using De Moivres theorem

An example in my book might help(didnt helped me at at all)

x^4-x^3+x^2-x+1

Sol:

The equation can be written as

x^4-x^3+x^2-x+1 = (x^5+1)/(x+1)
Hence the required roots of x^5+1 = 0 are same as those of (x^4-x^3+x^2-x+1)(x^5+1)

The equation (x^5+1) gives x^5 = -1 or x = (-1)^1/5

(......and so on)

Now what my trouble is how i can find equation like (x^5+1) for my problem stated at start of post?

I am newbie and poor in maths so little more explanation will help lot

6. Solve x^8+x^5+x^3+1 by using De Moivre`s theorem.

The given problem can be factorized as

x^5(x^3 + 1) + 1(x^3 + 1) = 0

(x^3+1)(x^5+1) = 0

Now solve.

7. thanks
sa-ri-ga-ma

I did it....