# Complex Numbers Mixed Operations Worksheet

## 6 problems

The complex numbers mixed operations worksheet covers addition, subtraction, multiplication, and division of complex numbers. Each operation follows specific rules: adding and subtracting combine real and imaginary parts separately, while multiplication uses distributive properties with $$i^2 = -1$$. Division involves multiplying by the conjugate to rationalize the denominator. Mastering these operations allows for seamless manipulation and simplification of complex number expressions, essential for advanced mathematical problem-solving.

Algebra 2
Real And Complex Numbers

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

• Working with complex numbers helps students think logically and solve problems by understanding and using different math rules.
• Complex numbers are critical in higher-level math like calculus, differential equations, and algebra, setting a strong foundation for advanced studies.
• Handling complex numbers strengthens algebra skills, such as expanding, simplifying, and solving equations.
• Learning to use complex numbers encourages critical thinking and problem-solving skills, as students work with abstract concepts and make sense of them.

## How to Complex Numbers Mixed Operations?

• To add or subtract complex numbers, add or subtract the real parts together and the imaginary parts together.
• To multiply two complex numbers, use the distributive property, multiply each part, and remember that the square of the imaginary unit is negative one.
• To divide one complex number by another, multiply the numerator and the denominator by the conjugate of the denominator. Then, simplify by combining like terms.
• The complex conjugate of a number changes the sign of the imaginary part. It is useful for simplifying division and other expressions involving complex numbers.

## Solved Example

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

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