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Mastering Complex Numbers: Dive into the World of Real and Imaginary Numbers

Explore the realm of complex numbers, from basic operations to advanced applications in various fields like electricity and economics. Learn to simplify, solve equations, and manipulate complex numbers in standard form effectively. Discover the significance of real, imaginary, and pure imaginary numbers in mathematical computations. Practice adding, subtracting, multiplying complex numbers following standard procedures. Enhance your skills with detailed examples and assignments.

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Mastering Complex Numbers: Dive into the World of Real and Imaginary Numbers

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  1. 5.7 Complex Numbers Goal: Understand and use complex numbers.

  2. Warm-up Simplify: Solve the equation:

  3. It is unfortunate that it is called imaginary because it is used in everything from electricity to economics. Simplify:

  4. Solve:

  5. A complex number is a number that can be written in a + bi form (standard form). a and b are real numbers. Complex Number System Real Numbers (b = 0) Imaginary Numbers (b ≠ 0) Pure Imaginary (a = 0)

  6. To add complex numbers, add their real parts and their imaginary parts separately. Example: Add or subtract. Write your answer in standard form.

  7. To multiply complex numbers, use the distributive property or FOIL. Remember: Example: Multiply. Write your answer in standard form.

  8. Since it cannot appear in the denominator of a fraction. To remove it, multiply both the numerator and denominator by the complex conjugate of the denominator. The complex conjugate of a + bi is a – bi. Write each expression in standard form:

  9. Assignment Pages 264-266 15-57 multiples of 3 87-97 odd

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