Multiply and simplify the following complex numbers: (4+4i)*(-2-5i) -x +1

Distribute terms: Distribute each term of the first complex number by each term of the second complex number. (4+4i) * (-2-5i) = 4*(-2) + 4*(-5i) + 4i*(-2) + 4i*(-5i)Multiply real and imaginary parts: Multiply the real parts and the imaginary parts. 4*(-2) = -8 (Real part) 4*(-5i) = -20i (Imaginary part) 4i*(-2) = -8i (Imaginary part) 4i*(-5i) = -20i^2 (Since i^2 = -1, this becomes a real part)Combine and simplify: Combine like terms and simplify. -8 (Real part from step 2) + (-20i - 8i) (Sum of Imaginary parts from step 2) - 20i^2 (Real part from step 2, remembering that i^2 = -1) -8 - 28i + 20(-1)Add real numbers: Simplify the expression by combining real parts and imaginary parts. -8 - 28i - 20Write final answer: Add the real numbers together. -8 - 20 = -28Write the final answer in the form of a complex number (a + bi). -28 - 28i

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Multiply and simplify the following complex numbers:

(4+4i)*(-2-5i)

-x
+1

Multiply and simplify the following complex numbers: $\newline$ $(4+4 i) \cdot(-2-5 i)$

View step-by-step help

Home

Math Problems

Grade 8

Multiply numbers written in scientific notation

Full solution

Q. Multiply and simplify the following complex numbers:

\newline

(4+4 i) \cdot(-2-5 i)

Distribute terms: Distribute each term of the first complex number by each term of the second complex number. $\newline$ $(4+4i) \times (-2-5i) = 4\times(-2) + 4\times(-5i) + 4i\times(-2) + 4i\times(-5i)$
Multiply real and imaginary parts: Multiply the real parts and the imaginary parts. $\newline$ $4 \cdot (-2) = -8$ (Real part) $\newline$ $4 \cdot (-5i) = -20i$ (Imaginary part) $\newline$ $4i \cdot (-2) = -8i$ (Imaginary part) $\newline$ $4i \cdot (-5i) = -20i^2$ (Since $i^2 = -1$ , this becomes a real part)
Combine and simplify: Combine like terms and simplify. $\newline$ $-8$ (Real part from step $2$ ) + $(-20i - 8i)$ (Sum of Imaginary parts from step $2$ ) - $20i^2$ (Real part from step $2$ , remembering that $i^2 = -1$ ) $\newline$ $-8 - 28i + 20(-1)$
Add real numbers: Simplify the expression by combining real parts and imaginary parts. $-8 - 28i - 20$
Write final answer: Add the real numbers together. $\newline$ $-8 - 20 = -28$
Write final answer: Add the real numbers together. $\newline$ $-8 - 20 = -28$ Write the final answer in the form of a complex number $a + bi$ . $\newline$ $-28 - 28i$