Simplify the expression to a + bi form: (3+10 i)(-4-6i) Answer:

Distribute Terms: Distribute each term in the first complex number by each term in the second complex number. We will use the distributive property (a+b)(c+d) = ac + ad + bc + bd. (3+10i)(-4-6i) = 3(-4) + 3(-6i) + 10i(-4) + 10i(-6i)Multiply Parts: Multiply the real parts and the imaginary parts. 3(-4) = -12 (real part) 3(-6i) = -18i (imaginary part) 10i(-4) = -40i (imaginary part) 10i(-6i) = 60 (real part, because i*i = -1)Combine Like Terms: Combine like terms. Combine the real parts: -12 + 60 Combine the imaginary parts: -18i - 40iPerform Addition: Perform the addition. Real parts: -12 + 60 = 48 Imaginary parts: -18i - 40i = -58iFinal Answer: Write the final answer in a + bi form. The simplified expression is 48 - 58i.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Simplify the expression to a + bi form:

(3+10 i)(-4-6i)
Answer:

Simplify the expression to a + bi form: $\newline$ $(3+10 i)(-4-6 i)$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Write a quadratic function from its zeros

Full solution

Q. Simplify the expression to a + bi form:

\newline

(3+10 i)(-4-6 i)

\newline

Answer:

Distribute Terms: Distribute each term in the first complex number by each term in the second complex number. $\newline$ We will use the distributive property $(a+b)(c+d) = ac + ad + bc + bd$ . $\newline$ $(3+10i)(-4-6i) = 3(-4) + 3(-6i) + 10i(-4) + 10i(-6i)$
Multiply Parts: Multiply the real parts and the imaginary parts. $\newline$ $3(-4) = -12$ (real part) $\newline$ $3(-6i) = -18i$ (imaginary part) $\newline$ $10i(-4) = -40i$ (imaginary part) $\newline$ $10i(-6i) = 60$ (real part, because $i*i = -1$ )
Combine Like Terms: Combine like terms. $\newline$ Combine the real parts: $-12 + 60$ $\newline$ Combine the imaginary parts: $-18i - 40i$
Perform Addition: Perform the addition. $\newline$ Real parts: $-12 + 60 = 48$ $\newline$ Imaginary parts: $-18i - 40i = -58i$
Final Answer: Write the final answer in $a + bi$ form. $\newline$ The simplified expression is $48 - 58i$ .