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Understanding Complex Numbers Operations

Learn about complex numbers, the real and imaginary parts, operations like addition and subtraction, practice problems, and using calculators for evaluation in this guide.

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Understanding Complex Numbers Operations

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  1. Complex Numbers Sec. 2.5

  2. First, try these… Evaluate:

  3. Definition:Complex Number A complex number is any number that can be written in the form where a and b are real numbers. The real number a is the real part, the real number b is the imaginary part, and a + bi is the standard form.

  4. Definition:Complex Number If b = 0, we have the real number a…  All real numbers are also complex numbers!!! If a = 0, the number becomes Imaginary Number Two complex numbers are equal if and only if their real and imaginary parts are equal.

  5. Operations with Complex Numbers If a + bi and c + di are two complex numbers, then Sum: Difference:

  6. Let’s Practice!!! Write the given expressions in the form bi, where b is a real number.

  7. Let’s Practice!!! Find the real numbers x and y that make the given equation true. x = 2, y = 5

  8. Let’s Practice!!! Write the sum or difference in standard form.

  9. Let’s Practice!!! Write the product in standard form. Foil!!! Can we use our calculator to evaluate operations with complex numbers?

  10. Let’s Practice!!! If , find and . Check with calculator!!!

  11. Let’s Practice!!! If , find and . Check with calculator!!!

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