Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations is part of Plus One Maths Notes. Here we have given Kerala Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations .

Board | SCERT, Kerala |

Text Book | NCERT Based |

Class | Plus One |

Subject | Maths Notes |

Chapter | Chapter 5 |

Chapter Name | Complex Numbers and Quadratic Equations |

Category | Plus One Kerala |

## Kerala Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations

- A number of the form z = x + iy where x, y ∈ R and i = is called a complex number.
- If a, b∈R, then provided a and b are not both negative.
- z = x + iy, Re (z) = x and Im (z) = y If Re (z) = 0 then z is purely imaginary If Im (z) = 0 then z is purely real.
- If z
_{1}= x_{1}+ iy_{1}and z_{2}= x_{2}+ i y_{2}, then x_{x}= z_{2}⇔ x_{1}= x_{2}and y_{1}= y_{2 } - If z = x + iy then conjugate of z, denoted by = x – iy
- If Z
_{1}– = x_{1}+ i y_{1}, and z_{2}= x_{2}, + i y_{2 }then Z_{1}+ Z_{2}⇔ (x_{1}+ x_{2}) + i (y_{1}+ y_{2})

Z_{1}. Z_{2}⇔ (x_{1 }x_{2}– y_{1}+ y_{2})+i (x_{1}y_{2 + }x_{2}y_{1}) - = Z
- z + = 2. Re (z)
- z + = 2i. Im (z)
- z = if z is purely real.
- z = – if z is purely imaginary.

**Geometrical Representation**

z = x + i y is represented by the point (x, y).OP is called modulus of z and | z |= . The angle θ is called argument or amplitude of z.

**Polar Representation of Complex Numbers**

Polar form of z = x + iy is z = r (cos θ + i sin θ ) where r=| z |= and argument 0 is obtained by solving x = r cosθ, y = rsinθ.The value of 0 such that

-n < θ < π is called principal argument of z.

- Solution of ax
^{2}+ bx + c = 0

where b^{2}– 4ac < 0 and a, b, c e R, a ≠0 is

We hope the Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations help you. If you have any query regarding Kerala Plus One Maths Notes Chapter 5 Complex Numbers and Quadratic Equations , drop a comment below and we will get back to you at the earliest.