Question

What is the value of the product (3-2i)(3+2i)?
5
9+ 41
9-41
13

Answer 1

13

Explanation:

The given expression is (3-2i)(3-2i)

This is of the form (a-b)(a+b)

This is equivalent to
`\[a^(2)-b^(2)\]`, where a = 3 and b=2i

=
`\[3^(2)-(2i)^(2)\]`

=
`\[9-4i^(2)\]`

But
`\[i^(2) = -1\]`

=
`\[9-4*(-1)\]`

=
`\[9+4\]`

=
`\[13\]`

Hence the value of the expression (3-2i)(3-2i) is 13.