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DeMoivre’s Theorem is a useful theorem in the mathematics of complex numbers. It enables complicated numbers in polar forms that might be raised to powers. It says that  as well as and

Students pursuing Mathematics find this theorem highly complicated and therefore they look for De Moivre’s Theorem assignment help. We have employed highly qualified Mathematicians who can offer the best math assignment solution. They help you to understand the complex calculations and offer you accurate solutions.

What is De Moivre’s Theorem?

According to De Moivre’s Theorem it is (cosθ+isinθ)n=cos(nθ)+isin(nθ). Multiplication of the two complex numbers adds their angles and multiplies their magnitudes. When both the factors are on a unit circle, it means the magnitude of two factors is 1 and the magnitude of a product is 1. When both the factors are on a unit circle, the product is a unit circle. The product’s angle shall be the addition of the angle of factors.

So, when a complex number is raised on a unit circle to the integer power nn then the angles of all factors are added. It means the original angle is multiplied by nn. This is the angle that ends up at the unit circle. This theorem tells us this. De Moivre’s Theorem can be used for finding the powers of the complex numbers and this theorem is extended for finding out roots of the complex numbers and also solve equations. BookMyEssay academic tutors are immensely experienced and they can provide you with help with assignment online on De Moivre’s Theorem.


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De Moivre’s Theorem can be used to find the power of the complex numbers

If z, a complex number in a polar form is written as

z=r(cos(θ)+isin(θ))z=r(cos?(θ)+isin?(θ))

then,

zn=rn(cos(nθ)+isin(nθ))zn=rn(cos?(nθ)+isin?(nθ))

and here n is an integer.

De Moivre’s Theorem can be often used to find the roots of a complex number

De Moivre’s theorem may be used for finding out the nth root of complex numbers

If z is a complex number

z=r(cos(θ)+isin(θ))z=r(cos?(θ)+isin?(θ))

then the nth roots are provided by

zk=r1/n(cos(θ+2kπn)+isin(θ+2kπn))zk=r1/n(cos?(θ+2kπn)+isin?(θ+2kπn))

here k=0,1,2,.... (n-1)

Applications of De Moivre’s Theorem

Some of the applications of De Moivre’s Theorem are stated in our De Moivre’s Theorem homework help services as follows:

  • To find out the expansions of the trigonometric functions

cosnθ=cosnθ−nC2cosn−2θsin2θ+nC4cosn−4θsin4θ……cos?nθ=cosnθ−nC2cosn−2θsin2θ+nC4cosn−4θsin4θ……

sinnθ=nC1cosn−1θsinθ−nC3cosn−3θsin3θ+nC5cosn−5θsin5θ−…….sin?nθ=nC1cosn−1θsin?θ−nC3cosn−3θsin3θ+nC5cosn−5θsin5θ−…….

 

 

  • To find out the roots of the complex numbers
  • To find out the complex solution of the algebraic equations

Importance of De Moivre’s Theorem

If the numbers are complex, which makes finding out their powers very challenging. Additionally, finding out the solutions or roots to the equations where the answers have complex numbers is very difficult. With the help of De Moivre’s Theorem, these problems can ve solved easily.

Finding out powers is very easy till the time the complex numbers are converted from the Standard form to the Polar Form. In doing these things, we just have to apply the De Moivre’s Theorem that is at times referred to as the De Moivre’s Formula or as Identity as pointed out by Wikipedia.

As mentioned in our writing assistance, when you ask "do my assignment for me on De Moivre’s Theorem," you can easily and quickly find the powers of the complex numbers, even if the exponent is negative. Similarly, if a complex number is raised to a power you can find all the roots. From the Fundamental Theorem of Algebra, all nonzero numbers have n-distinct roots. Thus the nth Root Theorem or the Complex Root Theorem.


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