COMPLEX NUMBERS | INTRODUCTION, DEFINITION OF COMPLEX NUMBERS, ALGEBRA OF COMPLEX NUMBER, CONJUGATE OF A COMPLEX NUMBER, PROPERTIES OF CONJUGATE OF A COMPLEX NUMBER | 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`