Question

What is DMT theorem class 9
Chapter: Circles

Answer 1

Answer:

In mathematics, de Moivre's formula states that for any real number x and integer n it holds that where i is the imaginary unit. The formula is named after Abraham de Moivre, although he never stated it in his works. The expression cos(x) + i sin(x) is sometimes abbreviated to cis(x).

Step-by-step explanation:

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Answer 2

Answer:

DMT theorem states that for any real number x, $(cos x + i sin x)^{n} = cos(nx) + i sin(nx)$ .

Step-by-step explanation:

DMT theorem also called as DeMoivre’s Theorem is one of the most important and useful theorems which connects complex numbers and trigonometry.

The name of the theorem is after the name of great Mathematician De Moivre, who made many contributions to the field of mathematics.

Mathematical Statement: DMT theorem states that $(cos x + i sin x)^{n} = cos(nx) + i sin(nx)$ for any real number x where n is a positive integer and i is the imaginary part, $i=\sqrt{-1}$.

In circles when we represent the coordinates in polar form i.e., $x = r cos \alpha$ and $y=rsin\alpha$, DMT theorem can be used to make calculations simpler.

We get $r=\sqrt[2]{x^{2} +y^{2} }$ and $tan\alpha =\frac{y}{x}$. It can be written as complex number i.e. $z=x+iy=r(cos\alpha +isin\alpha )$

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