# Multiply Complex Numbers Worksheet

## 6 problems

To multiply complex numbers, distribute each term and apply $$i^2 = -1$$. For instance, multiplying $$(2 + 3i)$$ by $$(4 - 2i)$$ involves calculating $$8 + 12i - 4i - 6 = 14 + 8i$$. This process is essential for mastering complex number multiplication. Further practice and guidance can be found in worksheets dedicated to multiply complex numbers to understand the process thoroughly.
Example: Multiply the complex numbers $$(1 + 2i)$$ and $$(3 - i)$$.

Algebra 2
Real And Complex Numbers

## How Will This Worksheet on "Multiply Complex Numbers" Benefit Your Student's Learning?

• Helps understand advanced math topics like complex analysis and differential equations.
• Enhances ability to solve problems involving real and imaginary numbers.
• Reinforces algebra through distributing and combining terms.
• Assists in solving complex equations in higher-level math and science.
• Develops critical thinking by carefully applying algebraic rules.

## How to Multiply Complex Numbers?

• Multiply each term in the first complex number by each term in the second complex number.
• Use the property $$i^2 = -1$$ to simplify $$i$$ terms.
• Add or subtract the real and imaginary parts separately.

## Solved Example

Q. Simplify.$\newline$$5(3 + 5i)$$\newline$Write your answer in the form $a + bi$.
Solution:
1. Distribute $5$: Distribute $5$ inside the parentheses. $5(3 + 5i) = (5 \times 3) + (5 \times 5i)$
2. Simplify expression: Simplify $(5 \times 3) + (5 \times 5i)$.$\newline$ $(5 \times 3) + (5 \times 5i) = 15 + 25i$

### What teachers are saying about BytelearnWhat teachers are saying

Stephen Abate
19-year math teacher
Carmel, CA
Any math teacher that I know would love to have access to ByteLearn.
Jennifer Maschino
4-year math teacher
Summerville, SC
“I love that ByteLearn helps reduce a teacher’s workload and engages students through an interactive digital interface.”
Rodolpho Loureiro
Dean, math program manager, principal
Miami, FL
“ByteLearn provides instant, customized feedback for students—a game-changer to the educational landscape.”