complex numbers

Complex Numbers in Mathematics

 

Suppose you want to solve an equation x2+1=0  then you will get x=√-1    which does not belongs to real number system. Leonhard Euler proposed to write √-1  as  i (iota)  and gave concept of  complex numbers.

Integral Power of i (iota)

i2=-1,    i3=-i,     i4=1
i5=i,    i6=-1,    i7=-1,    i8=1

Complex  Numbers

A complex number consists two parts a real part and imaginary  part of the form x+iy. Where x is real part and iy is imaginary part.

Let z1=x1+i y1 and z2=x2+i y be two complex numbers.
Then addition of two numbers, subtraction of a number from another number, multiplication of two numbers, division of one complex number by another number.

  • Addition of Complex Numbers

z1+z2 =x1+i y1 + x2+i y2

z1+z =(x+ x)+ i (y+ y)

  • Subtraction of a Complex Number from Another Number

z1-z2 =x1+i y1 -( x2+i y2)

z1+z =(x1 -x)+ i (y1 – y)

  • Multiplication of Complex Numbers

z1 *  z =  (x1+i y) *  (x2+i y2)

z1 *  z 2= ((x1 x2 – y1 y2) – i(x y2 – x2 y1)

  • Division of  Complex  Numbers

z1 ⁄ z2 = (x1 x2 +y1 y2)  /   x22 + y22   + i (x2 y1 – x1 y)  /  x22 + y22

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