This article has been authored by

Djeet,the Maths editor at Xamplified,who has over four years of experience in teaching Mathematics.His write-ups at Xamplified can truly be termed ‘Examplified’ as he breaks down complex maths concepts into simple how-to steps.

**Table Of Content**

## Brush Up Basics

### Step 1: Recap basic facts

- Argand Plane is used to represent the
**complex number**. The horizontal axis of Argand plane represents the real part while vertical axis represents the imaginary part of complex number. - The modulus of complex number is distance of a point P (which represents
**complex number**in Argand Plane) from the origin.

### Step 2: Plot the complex number in Argand plane

In geometrical representation, **complex number** z = (x + iy) is represented by a complex point P(x, y) on the complex plane or the Argand Plane. Join this point ‘P’ with the origin ‘O’. Let this ray be called OP.

Geometrical representation of **complex number** in Argand Plane

Depending upon the sign of real part ‘x’ and imaginary part ‘y’, complex point ‘P’ can exist in any quadrant.

### Step 3: Calculate the length of ray ‘OP’

The length OP is calculated using **Pythagoras Theorem**.

In Triangle OAP,

OP² = OA² + AP²

OP² = x² + y²

Therefore,

The length of OP is the modulus of **complex number** and is denoted by |z|.

## Observations to give you insight

- It does not matter in which quadrant complex number lies, its modulus will always be positive.
- Two different
**complex numbers**can have same modulus. For example 4 + i3, 4 – i3, -4 + i3, -4 – i3, 3 + i4, 3 – i4, -3 + i4 and -3 – i4 all have five as their modulus.