Our CBSE Notes for Algebra of Complex Numbers Class 11 maths 5. Complex Number and Quadratic Equations - CBSE Notes - Toppers Study is the best material for English Medium students cbse board and other state boards students.

# Algebra of Complex Numbers Class 11 maths 5. Complex Number and Quadratic Equations - CBSE Notes - Toppers Study

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## Algebra of Complex Numbers Class 11 maths 5. Complex Number and Quadratic Equations - CBSE Notes - Toppers Study

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### Algebra of Complex Numbers class 11 Mathematics Chapter 5. Complex Number and Quadratic Equations

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## 5. Complex Number and Quadratic Equations

### | Algebra of Complex Numbers |

## Algebra of Complex Numbers Class 11 maths 5. Complex Number and Quadratic Equations - CBSE Notes - Toppers Study

### 7. Algebra of Complex Numbers

*(A) Addition of Complex numbers*

*Let **z*_{1}* = **a **+ **ib **and **z*_{2}* = **c **+ **id **be any two complex numbers. Then, the sum **z*_{1}* + **z*_{2}* is defined as follows:*

*z*_{1}* + **z*_{2}* = (a+ib)+(c+id) = (**a **+ **c**) + **i **(**b **+ **d**), which is again a complex number.*

*Ex: **z*_{1}* =2 + i3 and z _{2} = 7 + i5*

*z _{1}+ z_{2} = (2+7) +i(3+5)*

* = 9+i8*

*Alternative Method: *

*z _{1}+ z_{2} = 2+i3 +7+i5*

* = 2+7+i3+i5*

* = 9+i(3+5)*

* = 9+i8 *

*(B) Subtraction of Complex Numbers*

*Given any two complex numbers **z*_{1}* and **z*_{2}*, the difference **z*_{1}* – **z*_{2}* is defined as follows:*

*z*_{1}* – **z*_{2}* = (a+ib) – (c+id) = (a–c)+i(b–d) *

*For example: **z*_{1}*= 4+i3, z _{2} =3 + i7*

*z*_{1}* – **z*_{2}* =(4–3)+i(3–7)= 1–i4 *

*Note: {4 and 3are like term and i3 and i7 are another like term}*

*Alternative Method: *

*z*_{1}* – **z*_{2}* =(4+i3) – (3+i7)*

* =4+i3 – 3 – i7*

* =4– 3+i3 – i7*

* =1+i(3 – 7)*

* =1-i4*

*(C) Multiplication of Complex numbers: *

*z _{1} × z_{2} = (a +ib) (c+id) *

* =a(c+id) +ib(c+id)*

* = ac + iad + ibc +(** –**bd)*

* = ac **–**bd +i(ad+bc)*

*For example: z _{1}= 2+3i, z_{2}=5 +2i*

*z _{1}× z_{2} = (2+3i)( 5 +2i)*

* = (2×5 – 3×2)+ i(2×2+3×5)*

* = 10 – 6 + i(4+15)*

* = 4 + 19i*

*Alternative Method: *

*z _{1}× z_{2} = (2+3i)( 5 +2i)*

* =2( 5 +2i) +3i( 5 +2i)*

* = 10 + 4i + 15i + 6i ^{2}*

* = 10 + 4i + 15i + 6(–1) *

* = 10 – 6 + 19i *

* = 4 + 19i *

*(D)Some Important identities: *

- (z
_{1}+ z_{2})^{2}= z_{1}^{2}+ 2 z_{1}z_{2}+ z_{2}^{2} - (z
_{1}– z_{2})^{2}= z_{1}^{2}– 2 z_{1}z_{2}+ z_{2}^{2} - (z
_{1}+ z_{2})^{3}= z_{1}^{3}+ 3 z_{1}^{2}z_{2}+ 3 z_{1}z_{2}^{2}+ z_{2}^{3} - (z
_{1}– z_{2})^{3}= z_{1}^{3}– 3 z_{1}^{2}z_{2}+ 3 z_{1}z_{2}^{2}– z_{2}^{3} - z
_{1}^{2}– z_{2}^{2}= (z_{1 }+ z_{2})( z_{1 }– z_{2})

##### Other Pages of this Chapter: 5. Complex Number and Quadratic Equations

4. Chapter 5. Complex Number and Quadratic Equations | The Modulus and Congugate of a Complex Number

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