Question

Find the product of the complex number and its conjugate. 3 + 3i

Answer 1

Hello,

(3+3i)(3-3i)=3²-3²i²=3²+3²=18

Answer 2

First, we are going to find the conjugate of our complex number. Remember that to find the conjugate of a complex number we just need to keep the real part and change the sing of the imaginary part.

We can infer from our problem that the real part of our complex number is 3 and its imaginary part is $3i$. We are going to keep the real part 3 and change the imaginary part from positive to negative, so our conjugate is $3-3i$.

Next, we are gong to multiply both the complex number and its conjugate using the distributive property:

$(3+3i)(3-3i)=(3*3)-(3*3i)+(3*3i)-(3i*3i)=9-9i+9i-9i^2=9-9i^2$

Remember that $i^2=\sqrt{-1}^{2} =-1$, so:

$9-9i^2=9-9(-1)=9+9=18$

We can conclude that the product of the multiplication of the complex number 3+3i and its conjugate, 3-3i, is 18.