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| A square root of a negative real number. |
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A number of the form a + bi, where the
real number a is called the real part a of a + bi, the real number b is called the imaginary part of a + bi, and i is √-1 |
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The complex numbers a + bi and a - bi
are complex conjugates of each other. |
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| Square Root of a Negative Real Number |
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| For any positive real number a, √-a = i√a |
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| Simplifying Imaginary Numbers |
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| Simplify the radical expression. Write new answer in ab + i form. |
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| Simplifying More Imaginary Numbers |
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Divide number by 4.
Take the remainder of that number and make it the exponent. |
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1066/4 = 266.5
Therefore, the remainder is 2.
i2 = -1 |
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76/4 = 19
Therefore, the remainder is 0.
i0 = 1 |
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Add like terms together.
Simplify. |
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5 + (-2) + 7i + 6i
3 + 13i |
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| Multiplying Complex Numbers |
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Multiply the real numbers.
Substitute -1 for i2
Simplify. |
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(5i)(-4i) = -20i2
-20(-1) 20 |
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| -6 + 10i - 9i + 15i(2) -6 + i + 15(-1) -15 - 6 + i -21 + i |
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24 - 18i - 20i +15i2
24 - 38i + 15(-1)
24 - 15 - 38i
9 - 38i |
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Rationalize denominator
FOIL
Simplify |
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| Equation Used When Making Matrix |
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