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Complex Numbers

Lesson 3.3

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By definition

Consider powers if i

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Now we can handle quantities that occasionally show up in mathematical solutions

What about

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Combine real numbers with imaginary numbers

a + bi

Examples

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Write these complex numbers in standard form a + bi

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Complex numbers can be combined with

addition

subtraction

multiplication

division

Consider

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Operations on Complex Numbers

Division technique

Multiply numerator and denominator by the conjugate of the denominator

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Possible result

Reset mode Complex format to Rectangular

Now calculator does desired result

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Complex Numbers on the Calculator

Operations with complex on calculator

Make sure to use the correct character for i. Use 2nd-i

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Consider

It is tempting to combine them

The multiplicative property of radicals only works for positive values under the radical sign

Instead use imaginary numbers

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Try It Out

Use the correct principles to simplify the following:

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Consider the expression under the radical in the quadratic formula

This is known as the discriminant

What happens when it is

Positive and a perfect square?

Positive and not a perfect square?

Zero

Negative ?

Return of the

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Consider the solution to

Note the graph

No intersections with x-axis

Using the solve and csolve functions

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Go to page:

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- The Imaginary Number
- Using
- Complex Numbers
- Try It Out
- Operations on Complex Numbers
- Complex Numbers on the Calculator
- Warning
- The Discriminant
- Example
- Fundamental Theorem of Algebra
- Conjugate Zeroes Theorem
- Assignment

- Understanding Heat Transfer, Conduction, Convection and Radiation
- Solar Energy
- Mechanical, Electromagnetic, Electrical, Chemical and Thermal
- Newton’s third law of motion
- Direct heat utilization of geothermal energy
- Space Radiation
- Newton’s laws of motion

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