Questions: Multiply. -6 i(-5+5 i) Write your answer as a complex number in standard

Solution Steps

To multiply the given complex numbers, apply the distributive property (also known as the FOIL method for binomials) to expand the expression. Simplify the result by combining like terms and using the fact that \(i^2 = -1\).

We start with the expression to multiply: \[ -6i(-5 + 5i) \] Here, we identify the complex numbers as \( a = -6i \) and \( b = -5 + 5i \).

Using the distributive property, we expand the expression: \[ -6i \cdot (-5) + (-6i) \cdot (5i) \] Calculating each term gives: \[ 30i - 30i^2 \]

Recall that \( i^2 = -1 \). Therefore, we can substitute: \[ -30i^2 = -30(-1) = 30 \] Now, we combine the terms: \[ 30 + 30i \]

Final Answer