Maths HL ( Dont Understand De Moivre's Theorom )

9de5q7tsr8u2im

Complex number chapter.

Can someone please help i understand the modulus, angles, polar form etc.

Moody_mona

Do you not understand what it does? Where it comes from? Or how to use it?

skippy1977

De Moivre's Theorem is a very useful tool to raise complex numbers to large powers (amongst other things)

For example if you have a complex number z=-2-2i and you want to raise it to the power of 5 you would have to do (-2-2i)(-2-2i)(-2-2i)(-2-2i)(-2-2i)...ouch!

With De Moivre's Theorem you simply convert the complex number into its polar form 2root2(cos5pi/4 + isin5pi/4) and then raise the modulus of 2root2 to the power of 5 and multiply each of the angles 5pi/4 by 5. Then use your calculator to convert this back into rectangular (cartesian) form.

cnocmhuiregranard.ie/wordpress/wp-content/uploads/2015/01/Complex.jpg

9de5q7tsr8u2im

Moody_mona wrote: »

Do you not understand what it does? Where it comes from? Or how to use it?

No
I know all addition subtraction multiplication division of complex numbers
Plotting on argand diagram
Finding modulus
Transformations
Equations with complex roots
Writing complex numbers in polar form

The example of de moivre theorom in our book is so confusing and its coming up in our pres but if it has anything to do with binomial expansion dont bother as we havent covered that yet,
Thanks!!

Moody_mona

No I wasn't trying to "list" the things you could understand, I just wanted you know what it was you didn't understand. As the poster above mentioned, it's a technique used to raise a complex to a certain number, and avoiding multiplying it out repeatedly.

The method is: convert a complex number from rectangular to polar form, and then "apply" de Moivres theorem. This means raising the modulus to the power given, and multiplying the argument by the number (multiplying not powering). From here it can be typed fairly easily into your calculator. There's another step then if the power is a fraction - do use know about this?

9de5q7tsr8u2im

Moody_mona wrote: »

No I wasn't trying to "list" the things you could understand, I just wanted you know what it was you didn't understand. As the poster above mentioned, it's a technique used to raise a complex to a certain number, and avoiding multiplying it out repeatedly.

The method is: convert a complex number from rectangular to polar form, and then "apply" de Moivres theorem. This means raising the modulus to the power given, and multiplying the argument by the number (multiplying not powering). From here it can be typed fairly easily into your calculator. There's another step then if the power is a fraction - do use know about this?

Oh right sorry think i do but forgot how to do it the answers i have in my copy make no sense to me except for the first and second step but then confused thanks anyway appreciate the help!

thelad95

If you look it up on Youtube, you can find thousands of tutorial videos on anything on the HL maths course. Here's one that seems good: