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 y2 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.
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Addition of Complex Numbers
z1+z2 =x1+i y1 + x2+i y2
z1+z2 =(x1 + x1 )+ i (y1 + y2 )
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Subtraction of a Complex Number from Another Number
z1-z2 =x1+i y1 -( x2+i y2)
z1+z2 =(x1 -x2 )+ i (y1 – y2 )
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Multiplication of Complex Numbers
z1 * z 2 = (x1+i y1 ) * (x2+i y2)
z1 * z 2= ((x1 x2 – y1 y2) – i(x1 y2 – x2 y1)
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Division of Complex Numbers
z1 ⁄ z2 = (x1 x2 +y1 y2) / x22 + y22 + i (x2 y1 – x1 y) / x22 + y22
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