### De Moivre's Theorem

We know that the trigonometrical form of a complex number

*is given by*

**z**

**z = r(cos theta + i sin theta)**where ,

**r = /z/ , theta = arg z**The product of two complex number is a complex number , As such

*is also a complex number .*

**n th power of (a+ib)**But the methods of ordinary Algebra do not provide us with any precious method for computing

*where*

**n th power of (a+ib)***may be an integer or fraction .*

**n**De Moivre's Theorem helps us to compute the value of

*by changing it in a trigonometrical form .*

**n th power of (a+ib)****The general enunciation of De Moivre's Theorem :-**

For all values of

*and*

**n***, real or complex ;*

**theta**

*is a value of*

**cos n theta + i sin n theta**

**n th power of cos theta + i sin theta**The theorem holds for real and non real complex values of

*and*

**theta**

**n**The expression

*is some times abbreviated to*

**cos theta + i sin theta**

**cos theta****So , De Moivre's Theorem is ;**

**n th power of cos theta + i sin theta**

**= cos n theta + i sin n theta**
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