Updated On: 11-2-2020
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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`
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