### Mathematics Class XI

Unit-I: Sets and Functions
Chapter 1: Sets
Unit-II: Algebra
Chapter 5: Binomial Theorem
Chapter 6: Sequence and Series
Unit-III: Coordinate Geometry
Chapter 1: Straight Lines
Chapter 2: Conic Sections
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability
Chapter 1: Statistics
Chapter 2: Probability

# Some important identities of Complex Numbers

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(i)

(ii)

(iii)

(iv)

(v)

Power of

In general, for any ,

Here, are roots of the equation , where we get two real roots, and and two imaginary roots and , by solving:

The Modulus of a Complex Number

Let be a complex number. Then, the modulus of , denoted by , is defined to be the non-negative real number i.e.,

Example:

Let

Conjugate of a Complex Number

Let , be a complex number. Then, the complex conjugate of , denoted by , is a complex number , i.e., .

Example:

If

NOTE:

(i) Let , be a complex number which is purely real, it has no imaginary part.

i.e.,

(ii) Let , be a complex number which is called purely imaginary, it have no real part.

i.e,

Some Important Properties:

(i) If then we get,

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