Simplify the expression to a + bi form: (-8-9i)(10-2i) Answer:

Apply Distributive Property: To simplify the expression (-8-9i)(10-2i), we will use the distributive property (also known as the FOIL method for binomials), which involves multiplying each term in the first complex number by each term in the second complex number.Multiply Real Parts: First, we multiply the real parts: (-8) * (10) = -80.Multiply Real and Imaginary Parts: Next, we multiply the real part of the first complex number by the imaginary part of the second complex number: (-8) * (-2i) = 16i.Multiply Imaginary Parts: Then, we multiply the imaginary part of the first complex number by the real part of the second complex number: (-9i) * (10) = -90i.Combine Terms: Finally, we multiply the imaginary parts: (-9i) * (-2i) = 18i^2. Since i^2 = -1, this simplifies to 18 * (-1) = -18.Now, we combine all the terms: -80 (from the first step) + 16i (from the second step) - 90i (from the third step) - 18 (from the fourth step).Combining like terms, we get: -80 - 18 + 16i - 90i = -98 - 74i.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify the expression to a + bi form:

(-8-9i)(10-2i)
Answer:

Simplify the expression to a + bi form: $\newline$ $(-8-9 i)(10-2 i)$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Precalculus

Find the roots of factored polynomials

Full solution

Q. Simplify the expression to a + bi form:

\newline

(-8-9 i)(10-2 i)

\newline

Answer:

Apply Distributive Property: To simplify the expression $(-8-9i)(10-2i)$ , we will use the distributive property (also known as the FOIL method for binomials), which involves multiplying each term in the first complex number by each term in the second complex number.
Multiply Real Parts: First, we multiply the real parts: $(-8) \times (10) = -80$ .
Multiply Real and Imaginary Parts: Next, we multiply the real part of the first complex number by the imaginary part of the second complex number: $(-8) \times (-2i) = 16i$ .
Multiply Imaginary Parts: Then, we multiply the imaginary part of the first complex number by the real part of the second complex number: $(-9i) \times (10) = -90i$ .
Combine Terms: Finally, we multiply the imaginary parts: $(-9i) \times (-2i) = 18i^2$ . Since $i^2 = -1$ , this simplifies to $18 \times (-1) = -18$ .
Combine Terms: Finally, we multiply the imaginary parts: $(-9i) \times (-2i) = 18i^2$ . Since $i^2 = -1$ , this simplifies to $18 \times (-1) = -18$ .Now, we combine all the terms: $-80$ (from the first step) + $16i$ (from the second step) - $90i$ (from the third step) - $18$ (from the fourth step).
Combine Terms: Finally, we multiply the imaginary parts: $(-9i) \times (-2i) = 18i^2$ . Since $i^2 = -1$ , this simplifies to $18 \times (-1) = -18$ .Now, we combine all the terms: $-80$ (from the first step) + $16i$ (from the second step) - $90i$ (from the third step) - $18$ (from the fourth step).Combining like terms, we get: $-80 - 18 + 16i - 90i = -98 - 74i$ .