CBSE Class 11-Mathematics: Addition of Complex Numbers (Formulas) (For CBSE, ICSE, IAS, NET, NRA 2022)

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Complex numbers are the numbers of the form where and a and b are real numbers.

Definition:-

Complex numbers are defined as an ordered pair of real numbers like where

and both and are real numbers and is known as real part of complex number and is known as imaginary part of the complex number.

Addition of complex numbers

Let and then

Subtraction

Multiplication

Division

To divide complex number by another, first write quotient as a fraction. Then reduce the fraction to rectangular form by multiplying the numerator and denominator by the complex conjugate of the denominator making the denominator real.

Points to remember

1. Complex conjugate of is

2. Modulus of the absolute value of is denoted by and is defined by

3. Let r be any non-negative number and any real number. If we take and then, which is the modulus of and which is the argument or amplitude of and is denoted by we also have

4. Argument of a complex number is not unique since if is the value of argument then are also values of the argument. Thus, argument of complex number can have infinite number of values which differ from each other by any multiple of ? .

5. is not defined.

6. Argument of positive real number is zero.

7. Argument of negative real number is

8. Properties of moduli:-