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Chapter 1 Complex Number

1.1 Introduction : A complex number, in mathematics, is a number consisting of a real number part and an imaginary number part.  It is written in the form a + bi, where a and b are real numbers, and i is the square root of minus one. Complex numbers are useful abstract quantities that can be used in calculations

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1.1.1 Imaginary Numbers: Numbers whose square roots are negative are known as Imaginary numbers.

Example: √-1 , √-2

Imaginary number √-1 is denoted by the greek letter ‘i’ called iota.

1.1.2 Powers of i: i0 = 1; i2 = -1 ; i3 = -i ; and i4 = 1

For any two real numbers a & b;

√a × √b = √ab is true only when at least one of a and b is either 0 or positive.


√-a ×√-b = (i√a)(i√b) = i2 √ab = - √ab

Where a and b are positive real numbers.

In a complex number

Z = a + ib

a and b are the real numbers i is the imaginary number. a is the real part and b is the imaginary part and are written as ;

Re(z) = a


Im(z) = b

The set of complex numbers is given by:-

C = {z:z= a + ib, where a, b є R}

Example: In (4 +6i)

Re(z) = 4


Im(z) = 6

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