# Complex Numbers

## Polar Form of Complex Numbers with Examples

Here you will learn what is the polar form of complex numbers with examples. Let’s begin –  Polar Form of Complex Numbers Let z = x + iy be a complex number represented by a point P(x, y) in the argand plane. Then by the geometrical representation of z = x + iy, we have …

## Amplitude of a Complex Number

Here you will learn how to find argument or amplitude of a complex number with examples. Let’s begin –  Amplitude of a Complex Number (Argument of Complex Number) Let z = x + iy, Then, The angle $$\theta$$ which OP makes with the positive direction of x-axis in anticlockwise sense is called the argument or …

## How to Find Square Root of Complex Number

Here you will learn what is square root and how to find square root of complex number with examples. Let’s begin – How to Find Square Root of Complex Number Let a + ib be a complex number such that $$\sqrt{a + ib}$$ = x + iy, where x and y are real numbers. Then, …

## How to Find the Reciprocal of a Complex Number

Here you will learn how to find the reciprocal of a complex number with examples. Let’s begin –  How to Find the Reciprocal of a Complex Number The reciprocal is also called multiplicative inverse. Let z = a + ib be a non-zero complex number. Then $$1\over z$$ = $$1\over a + ib$$ Multiply numerator …

## How to Find the Modulus of a Complex Number

Here you will learn how to find the modulus of a complex number and properties of modulus with examples. Let’s begin –  How to Find the Modulus of a Complex Number The modulus of a complex number z = a + ib is denoted by | z | and is defined as | z | …

## How to Find the Conjugate of a Complex Number

Here you will learn how to find the conjugate of a complex number and properties of conjugate with examples. Let’s begin –  How to Find the Conjugate of a Complex Number Let z = a + ib be a complex number. Then the conjugate of z is denoted by $$\bar{z}$$ and is equal to a …

## Division of Complex Numbers

Here you will learn what is the division of complex numbers with examples. Let’s begin – Division of Complex Numbers The division of a complex number $$z_1$$ by a non-zero complex number $$z_2$$ is defined as the multiplication of $$z_1$$ by the multiplicative inverse of $$z_2$$ and is denoted by $$z_1\over z_2$$. Thus, $$z_1\over z_2$$ …

## Multiplication of Complex Numbers – Properties and Examples

Here you will learn multiplication of complex numbers and its properties with examples. Let’s begin – Multiplication of Complex Numbers Let $$z_1$$ = $$a_1 + ib_1$$ and $$z_2$$ = $$a_2 + ib_2$$ be two complex numbers. Then the multiplication of $$z_1$$ with $$z_2$$ is denoted by $$z_1 z_2$$ and is defined as the complex number …

## Addition of Complex Numbers – Properties and Examples

Here you will learn subtraction and addition of complex numbers and its properties with examples. Let’s begin –  Addition of Complex Numbers  Let $$z_1$$ = $$a_1 + ib_1$$ and $$z_2$$ = $$a_2 + ib_2$$ be two complex numbers. Then their sum $$z_1 + z_2$$ is defined as the complex number $$(a_1 + a_2)$$  + i\((b_1 …

## Complex Number Class 11

Here you will learn what is the complex number class 11 and equality of complex numbers with examples. Let’s begin –  Complex Number Class 11 If a, b are two real numbers, then a number of the form a + ib is called aa complex number. Example : 7 + 2i, -1 + i, 3 …