Question

(7+9i)(7-9i) what is my answer in a+bi form

Answer 1

We have here a multiplication of two complex numbers. However, we can use the following rule to deal with this question:

`(a+b)\cdot(a-b)=a^2-b^2`

Or equivalently:

`(a+bi)\cdot(a-bi)=a^2+b^2`

We will do it step by step:

`(7+9i)\cdot(7-9i)=(7)^2-(9i)^2=49-9^2(i)^2^{}`

Then, we have that i²=-1.

`49-9^2(-1)=49+81=130`

Therefore, we have that:

`(7+9i)(7-9i)=130`

[Notice that the imaginary part of this complex number is equal to 0i = 0.]