Use Conjugates to Find Moduli
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.
Find the modulus of 5 + 2i.
Ex. 1: Find the modulus of 5 + 2i.
First, find the conjugate.
5 - 2i
Second, multiply the complex number by its conjugate.
(5 + 2i)(5 - 2i)
25 + 10i - 10i - 4i2
The middle terms will cancel out. Then substitute -1 in for i2.
25 - 4(-1)
29
The last step is to take the square root of the answer.
Answer:
