Complex Numbers Mixed Operations Worksheet

Algebra 2
Real And Complex Numbers

Total questions - 6

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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(15i)5(1 - 5i)5\newlineWrite your answer in the form a+bia + bi.\newline______
Solution:
  1. Distribute 55: Distribute 55 to both terms inside the parentheses.\newline (15i)5=(1×5)+(5i×5)(1 - 5i)5 = (1 \times 5) + (-5i \times 5)
  2. Simplify expression: Simplify (1×5)+(5i×5)(1 \times 5) + (-5i \times 5).\newline (1×5)+(5i×5)=525i(1 \times 5) + (-5i \times 5) = 5 - 25i
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About Worksheet

Algebra 2
Real And Complex Numbers

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.

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