Download Nov 77:57 AM 4.6 Perform Operations with Complex Numbers

4.6 Perform Operations with Complex Numbers
-The imaginary unit i is defined as i = √-1 .
- Using this, we get _________.
- If r is a positive real number, then √-r =i√r .
Examples: Solve.
1.) x2 = -4
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2.) x2 = -54
3.) 9 - 4y2 = 57
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4.) 3p2 + 7 = -9p2 + 4
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-Complex number in standard form: A number of
the form a + bi, where a and b are real numbers.
Examples: Write the expression as a complex
number in standard form.
1.) (6 - 3i) + (5 + 4i)
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2.) (8 + 20i) - (-8 + 12i)
3.) 6i(3 + 2i)
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4.) (5 - 7i)(-4 - 3i)
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-Conjugate: The conjugate of a + bi is a - bi.
5.) -2 - 5i
3i
6.) 7 + 4i
2 - 3i
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7.) (4 + 3i) - (4 +6i)
(3 -i) + (8 + 4i)
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Imaginary
b
a + bi
Complex Plane
a
Real
Examples: Plot the numbers in the same complex plane.
-5i , 3 + 2i , 7 , 5 - 5i
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-Absolute value of a complex number:
If z = a + bi, then z = √a2 + b2 .
Examples: Find the absolute value of each complex
number.
1.) 4 + 3i
2.) -1 - 6i
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4.6 ICE
Simplify and write in standard form.
1.) (4 + 8i) - (9 - 4i)
2.) 4i(3i - 1)
3.) (3 - 5i)(6 + 2i)
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