Question

when -3 - 2i is multiplied by its conjugate, the result is

1. -13
2. -5
3. 5
4. 13

Explanation:

Step1: Find the conjugate of \(-3 - 2i\)

The conjugate of a complex number \(a + bi\) is \(a - bi\), so the conjugate of \(-3 - 2i\) is \(-3 + 2i\).

Step2: Multiply the complex number and its conjugate

We use the formula \((a + bi)(a - bi)=a^2 + b^2\) (since \(i^2=-1\), and when we expand \((a + bi)(a - bi)=a^2 - abi + abi - b^2i^2=a^2 + b^2\)). Here, \(a = -3\) and \(b=-2\), so we calculate \((-3 - 2i)(-3 + 2i)=(-3)^2-(-2)^2i^2\)? Wait, no, more accurately, using the formula \((x + y)(x - y)=x^2 - y^2\), where \(x=-3\) and \(y = 2i\). So \((-3)^2-(2i)^2=9 - 4i^2\). Since \(i^2=-1\), this becomes \(9-4\times(-1)=9 + 4 = 13\).

Answer:

1. 13