1. Module 11: Lesson 11.1 Solving Quadratic Equations by Taking Square Roots

3. Descartes was the first to use the term “imaginary” number in 1637
Descartes was the first to use the term “imaginary” number in However, the concept was invented much earlier by Gerolamo Cardano in the 16th century, but it was not widely accepted until the work of Leonhard Euler (1707–1783) and Carl Friedrich Gauss (1777–1855).
Engineers use complex numbers in studying stresses and strains on rays and in studying resonance occurrences in structures as different as tall buildings and suspension bridges. The complex numbers come up when we see for the eigenvalues and eigenvectors of a matrix. The eigenvalues are the roots of the assured polynomial equation related with a matrix. The matrices can be quite large, possibly by , and the related polynomials which is of very high degree. Complex numbers are used in studying the stream of liquids around hindrances, such as the flow around a pipe.

4. Reactance (Imaginary) Impedance (Complex) Real Power (Real)
­­­Application to electrical/electronics engineering
Resistance (Real)
Reactance (Imaginary)
Impedance (Complex)
Real Power (Real)
Reactive Power (Imaginary)
Complex Power (Complex)
See page 539

5. Complex Numbers
Imaginary
Numbers
Natural number
Whole number
Integer
Rational number
Examples: 1/3, 1/2, 3/7, 5/11, etc…
Irrational number
Examples:
Imaginary number
Examples: 2i, -3i, 1/3i, -1/2i, etc…
Complex number
Examples: 2, -7i, 5 + 2i, -3i - i, -2i = 4, etc…

6. Examples of Imaginary Numbers
You Tube:
Imaginary Numbers
Examples of Imaginary Numbers
Square each of these imaginary numbers

8. Solve Each