Use Conjugates to Find Moduli
The modulus of a complex number is the square root of the product of a complex number and it's conjugate.
To break this down, to find the modulus of a complex number:
- multiply the complex number by its conjugate, then take the square root of the answer
Example 1: Find the modulus of 4 - 3i.
First find the conjugate.
Second, multiply the complex number by its conjugate.
(4 - 3i)(4 + 3i)
+ i - i - i2
The middle terms will cancel out. Then substitute -1 in for i2.
16 - 9(-1)
16 + 9
25
The last step is to take the square root of the answer.
√25 = 5
The modulus of 4 - 3i is 5.
