Question

lesson: multiplying complex numbers
simplify: (-3 + i)(1 + 4i) (type your final answer in the box. do not put any spaces)

Explanation:

Step1: Use distributive property (FOIL)

Multiply each term in the first complex number by each term in the second:
$(-3)(1) + (-3)(4i) + i(1) + i(4i)$

Step2: Simplify each term

• $(-3)(1) = -3$
• $(-3)(4i) = -12i$
• $i(1) = i$
• $i(4i) = 4i^2$ (and recall $i^2 = -1$)

Step3: Substitute $i^2 = -1$ and combine like terms

$4i^2 = 4(-1) = -4$
Now combine all terms:
$-3 - 12i + i - 4$
Combine real parts: $-3 - 4 = -7$
Combine imaginary parts: $-12i + i = -11i$

Answer:

-7-11i