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College Algebra Chapter 1 Equations and Inequalities
Section 1.3 Complex Numbers
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1. Simplify Imaginary Numbers
2. Write Complex Numbers in the Form a + bi 3. Perform Operations on Complex Numbers
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Simplify Imaginary Numbers
and If b is a positive real number, then
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Examples 1 – 4: Write each expression in terms of i and simplify: 1. 2. 3. 4.
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Examples 5 – 7: Write each expression in terms of i and simplify: 5. 6. 7.
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Example 8: Multiply
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Example 9: Multiply
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Example 10: Divide
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1. Simplify Imaginary Numbers
2. Write Complex Numbers in the Form a + bi 3. Perform Operations on Complex Numbers
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Write Complex Numbers in the Form a + bi
Given real numbers a and b, a number written in the form a + bi is called a complex number. a is the real part b is the imaginary part
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Examples 11 – 13: Simplify and write the result in standard form a + bi. –5 i 13.
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Examples 14, 15: Simplify and write the result in standard form a + bi. 14. 15.
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1. Simplify Imaginary Numbers
2. Write Complex Numbers in the Form a + bi 3. Perform Operations on Complex Numbers
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Perform Operations on Complex Numbers
Powers of i : Every fourth power of i equals 1.
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Perform Operations on Complex Numbers
To simplify a power of i, write the expression as i to a power of 4 multiplied by
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Examples 16 – 18: Simplify: 16. 17. 18.
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Perform Operations on Complex Numbers
To add or subtract complex numbers, add or subtract their real parts, and add or subtract their imaginary parts.
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Examples 19, 20: 19. 20.
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Perform Operations on Complex Numbers
Multiply complex numbers as you would multiply polynomials. Remember
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Example 21:
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Example 22:
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Example 23:
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Example 24:
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Perform Operations on Complex Numbers
The expressions a + bi and a – bi are called complex conjugates. The product of complex conjugates is a real number.
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Perform Operations on Complex Numbers
To divide complex numbers, make the denominator a real number so the quotient can be written in the form a + bi.
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Example 25: Divide and write the result in the form a + bi.
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Example 26: Divide and write the result in the form a + bi.
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Example 27: Divide and write the result in the form a + bi.
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Example 28: Divide and write the result in the form a + bi.
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