Simplify the expression to a + bi form: (-1-4i)(2+8i) Answer:

Distribute Terms: Distribute each term in the first complex number by each term in the second complex number. (-1-4i)(2+8i) = (-1 * 2) + (-1 * 8i) + (-4i * 2) + (-4i * 8i)Perform Multiplication: Perform the multiplication for each term. (-1 * 2) = -2 (-1 * 8i) = -8i (-4i * 2) = -8i (-4i * 8i) = -32i^2 (Remember that i^2 = -1)Substitute and Combine: Substitute i^2 with -1 and combine like terms. -2 + (-8i) + (-8i) + (-32 * -1) -2 - 8i - 8i + 32Combine Real and Imaginary: Combine the real parts and the imaginary parts. Real part: -2 + 32 = 30 Imaginary part: -8i - 8i = -16iFinal Answer: Write the final answer in a + bi form. 30 - 16i

Home

Math Problems

Algebra 2

Simplify variable expressions using properties

Full solution

Q. Simplify the expression to a + bi form:

\newline

(-1-4 i)(2+8 i)

\newline

Answer:

Distribute Terms: Distribute each term in the first complex number by each term in the second complex number. $\newline$ $(-1-4i)(2+8i) = (-1 \times 2) + (-1 \times 8i) + (-4i \times 2) + (-4i \times 8i)$
Perform Multiplication: Perform the multiplication for each term. $\newline$ $(-1 \times 2) = -2$ $\newline$ $(-1 \times 8i) = -8i$ $\newline$ $(-4i \times 2) = -8i$ $\newline$ $(-4i \times 8i) = -32i^2$ (Remember that $i^2 = -1$ )
Substitute and Combine: Substitute $i^2$ with $-1$ and combine like terms. $\newline$ $-2 + (-8i) + (-8i) + (-32 \times -1)$ $\newline$ $-2 - 8i - 8i + 32$
Combine Real and Imaginary: Combine the real parts and the imaginary parts. $\newline$ Real part: $-2 + 32 = 30$ $\newline$ Imaginary part: $-8i - 8i = -16i$
Final Answer: Write the final answer in $a + bi$ form. $\newline$ $30 - 16i$