Element mathematics of class 11th solutions pdf download free chapter - 5 complex number - studymashup

Element of Mathematics Solutions of Class 11th 


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Chapter - 5

Important Theory

Complex Numbers

Definitions. A number of the form a + ib, where a and b are any real numbers and i = √-1, is  called  a complex number and is generally  denoted by z . Thus z  =a + ib.


'a' is called its real part and is denoted as Re (a + ib ) or Re(z) and 'b' os called imaginary part  and is denoted as Im (a + ib ) or Im (z).

Purely real and Purely Imaginary Numbers 

In case  = 0 , the number a + ib reducesto 0 + ib or 'ib' and is called a purely or wholly imaginary number . In case  b = 0 , the number becomes a + i0  i .e. , 'a' which os a real number anf is called a purely real number. A complex number a + ib is zero if both a and b are zero.

This a complex  number z is said to be

(a) purely real if Im (z) =0

and (b) purely imaginary if Re (z)  = 0.



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