Learn How to Calculate Modulus of Complex Number - Tutorial

Learn How to Modulus of complex number - Definition, Formula and Example

Definition:

Modulus of a complex number is the distance of the complex number from the origin in a complex plane and is equal to the square root of the sum of the squares of the real and imaginary parts of the number.

Formula:

|z| = |a + bi| = √a2 + b2
where
a,b - real number, i - imaginary number
Example:

The modulus of complex number z = 7 + 5i

Given,

a=7, b=5 i.e. z = 7 + 5i

To find,

Find Modulus of complex number. |z|,

Solution
Step 1:

Substitute the given value of a, b in the formula |z|,

|z| = |a + bi| = √a2 + b2
|z| = |7 + 5i| = √72 + 5 2
|z| = √74
|z| = 8.602325267

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