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2.25**Why we need Complex Number ?**

**Algorithm to find integral exponents of iota and generalize in terms of 4n+1 ; 4n; 4n+2**

**Definition Of Complex Numbers**

**Equality of complex numbers**

**Addition of complex number and their properties**

**Subtraction of complex numbers**

**multiplication of two complex no. and their properties**

**Division of two complex number**

**Conjugate of a complex no and its properties. If `z, z_1, z_2` are complex no.; then :-
(i) `bar(barz)=z` (ii)`z+barz=2Re(z)`(iii)`z-barz=2i Im(z)` (iv)`z=barz hArr z` is purely real (v) `z+barz=0implies` z is purely imaginary (vi)`zbarz=[Re(z)]^2+[Im(z)]^2`**

**Properties of a complex no. If `z;z_1;z_2` are complex no.; then (vii)`bar(z_1+z_2)=barz_2+barz_1` (viii)`bar(z_1-z_2)=barz_1-barz_2` (ix)`bar(z_1z_2)=barz_1barz_2` (x) `(barz_1)/z_2=barz_1/barz_2` where `z_2!=0`**