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Complex Numbers

Complex Numbers. Complex Numbers. The imaginary unit i is defined as. Example. Complex Numbers. The set of all numbers in the form a + b i with real numbers a and b , and i , the imaginary unit, is called the set of complex numbers.

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Complex Numbers

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  1. Complex Numbers

  2. Complex Numbers The imaginary unit i is defined as

  3. Example

  4. Complex Numbers • The set of all numbers in the form a + bi with real numbers a and b, and i, the imaginary unit, is called the set of complex numbers. • The real number a is called the real part, and the real number b is called the imaginary part, of the complex number a + bi.

  5. Equality of Complex Numbers • a+bi = c+di if and only if a = c and b = d

  6. Adding and Subtracting Complex Numbers Multiplying Complex Numbers

  7. Example Simplify:

  8. Example Multiply:

  9. Conjugate of a Complex Number The complex conjugate of the number a + bi is a - bi, and visa-versa. The product of a complex number and its conjugate is a real number.

  10. Example Rationalize:

  11. For any positive real number b, the principal square root of the negative number -b is defined by Principal Square Root of a Negative Number

  12. Example Simplify:

  13. Quadratic Formula

  14. Examples Solve:

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