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Complex Numbers. The imaginary unit i is defined as.

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Presentation on theme: "Complex Numbers. The imaginary unit i is defined as."— Presentation transcript:

1 Complex Numbers

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

12 Example Simplify:

13 Quadratic Formula

14 Examples Solve:


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