Questions: Multiply: (-3+2 i)(5-i) -17+13 i 2+i 13-13 i -13+13 i

Solution Steps

To multiply two complex numbers, use the distributive property (also known as the FOIL method for binomials). Multiply each part of the first complex number by each part of the second complex number, and then combine like terms. Remember that \(i^2 = -1\).

We are given two complex numbers: \((-3 + 2i)\) and \((5 - i)\).

To multiply these complex numbers, we use the distributive property: \[ (-3 + 2i)(5 - i) = (-3) \cdot 5 + (-3) \cdot (-i) + (2i) \cdot 5 + (2i) \cdot (-i) \]

Calculate each term:

• \((-3) \cdot 5 = -15\)
• \((-3) \cdot (-i) = 3i\)
• \((2i) \cdot 5 = 10i\)
• \((2i) \cdot (-i) = -2i^2\)

Since \(i^2 = -1\), we have: \[ -2i^2 = -2(-1) = 2 \]

Combine the real and imaginary parts: \[ -15 + 3i + 10i + 2 = (-15 + 2) + (3i + 10i) = -13 + 13i \]

Final Answer