Complex Number: ISC Class 11 Maths Understanding solutions Chapter-5. Step by step Solutions of ML Aggarwal ISC Class-11 Mathematics with Exe1.1, Exe-1.2, Exe-1.3, Exe-1.4, Exe-1.5, Exe-1.6, Exe-1.7, and Chapter Test Questions. Visit official Website CISCE for detail information about ISC Board Class-11 Mathematics..

## Complex Number: ISC Class 11 Maths Understanding solutions

Board | ISC |

Class | 11 |

Subject | Mathematics |

Chapter-5 | Complex Numbers |

Session | 2024-25 |

Topics | Solutions of ML Aggarwal |

**Complex Numbers**

A complex number is a number that can be expressed in the form p + iq, where p and q are real numbers, and i is a solution of the equation

**General form of Complex Number: z = p + iq**

- p is known as the real part, denoted by Re z
- q is known as the imaginary part, denoted by Im z

#### Algebra of Complex Numbers

**Addition of complex numbers : **Let z_{1} = m + ni and z_{2} = o + ip be two complex numbers. Then, z_{1} + z_{2} = z = (m + o) + (n + p)i, where z = resultant complex number. For example, (12 + 13i) + (-16 +15i) = (12 – 16) + (13 + 15)i = -4 + 28i.

- The sum of complex numbers is always a complex number (closure law)
- For complex numbers z
_{1}and z_{2}: z_{2}+ z_{1}= z_{1}+ z_{2}(commutative law) For complex numbers z_{1}, z_{2}, z_{3}: (z_{1}+ z_{2}) + z_{3}= z_{1}+ (z_{2}+ z_{3}) [associative law]. - For every complex number z, z + 0 = z [additive identity]
- To every complex number z = p + qi, we have the complex number -z = -p + i(-q), called the negative or additive inverse of z. [z + (–z) = 0]

**Difference of complex numbers : **Let z_{1} = m + ni and z_{2} = o + ip be two complex numbers, then z_{1} – z_{2} = z_{1} + (-z_{2}). For example, (16 + 13i) – (12 – 1i) = (16 + 13i) + (-12 + 1i ) = 4 + 14i and (12 – 1i) – (16 + 13i) = (12 – 1i) + ( -16 – 13i) = -4 – 14i

**Multiplication of complex numbers : **Let z_{1} = m + ni and z_{2} = o + ip be two complex numbers then, z_{1} × z_{2} = (mo – np) + i(no + pm). For example, (2 + 4i) (1 + 5i) = (2 × 1 – 4 × 5) + i(2 × 5 + 4 × 1) = -22 + 14i The product of two complex numbers is a complex number (closure law)

#### The Modulus and Conjugate of Complex Numbers

Let z = m + in be a complex number. Then, the modulus of z, denoted by |z| =

is the distance between the point (m, n) and the origin (0, 0). The x-axis is termed as the real axis and the y-axis is termed as the imaginary axis.

To know more about Modulus and Conjugate of Complex Numbers

**Exe-5.1**

Complex Numbers ML Aggarwal ISC Class-11 Maths Ch-5

**Exe-5.2**

Complex Numbers ML Aggarwal ISC Class-11 Maths Ch-5

**Exe-5.3**

Complex Numbers ML Aggarwal ISC Class-11 Maths Ch-5

**Exe-5.4**

Complex Numbers ISC Class-11 Maths Ch-5

**Exe-5.5**

**Exe-5.6**

ML Aggarwal ISC Class-11 Maths Ch-5

**Exe-5.7**

Complex Numbers ISC Class-11 Maths Ch-5

**Chapter Test**

Ch-5 Complex Numbers of ML Aggarwal ISC Class-11 Maths

-: End of Complex Number: ISC Class 11 Maths Understanding solutions :-

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