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Complex Numbers

This section delves into the concept of imaginary and complex numbers, which simplify radicals that lack real solutions. A complex number is expressed in standard form, comprising a real part and an imaginary part. It covers how to find square roots of various numbers, solve equations by equating real and imaginary components, and perform arithmetic operations such as addition, subtraction, and multiplication of complex numbers. Practical examples illustrate these techniques, enhancing comprehension of solving quadratic equations and understanding zeros of quadratic functions.

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Complex Numbers

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  1. Complex Numbers Section 3.2 Beginning on page 104

  2. Imaginary Numbers and Complex Numbers Imaginary numbers allow us to simplify radicals with no real solutions. A complex number written in standard form is a number where and are real numbers. The number is the real part, and the number is the imaginary part. Real Numbers: Complex Numbers: Pure Imaginary Numbers:

  3. Examples 1 and 2 Example 1: Find the square root of each number a) b) c) Example 2: Find the values of x and y that satisfy the equation ** Set the real parts equal to each other, set the imaginary parts equal to each other. Solve the resulting equations. **

  4. The Sums and Differences of Complex Numbers To add (or subtract) two complex numbers, add (or subtract) their real parts and their imaginary parts separately. Example 3:

  5. Multiplying Complex Numbers Example 5: Multiply. Write the answer in standard form. a) b) ** **

  6. Solving Quadratic Equations Example 6: Solve a) b) 18

  7. Finding Zeros of Quadratic Functions Example 7: Find the zeros of The zeros of the function are and

  8. Practice Find the square root of the number. 2) 3) 4) Find the values of x and y that satisfy the equation. 5) 6) Perform the operation. Write the answer in standard form. 8) 9) 10) 11) 12) 13) Answers: 1) 2) 3) 4) 5) 6) 8) 9) 10) 11) 12) 13)

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