# How do you find the product of the complex number and its conjugate #1 + 3i#?

##### 1 Answer

Dec 24, 2015

You can use the identity

#(1+3i)(1-3i) = 1^2+3^2 = 1+9 = 10#

#### Explanation:

Notice that:

#(a+bi)(a-bi) = a^2-(bi)^2 = a^2-i^2b^2 = a^2+b^2#

So we can deduce:

#z bar(z) = "Re"(z)^2+"Im"(z)^2#

for any Complex number