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Define complex numbers.

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Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit, defined as i = √(-1).

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CCSS.HSN.CN.A.1

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What is the formula for adding complex numbers?

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To add complex numbers, (a + bi) + (c + di) = (a + c) + (b + d)i.

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CCSS.HSN.CN.A.2

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What is the formula for subtracting complex numbers?

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To subtract complex numbers, (a + bi) - (c + di) = (a - c) + (b - d)i.

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CCSS.HSN.CN.A.2

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How do you multiply complex numbers?

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To multiply complex numbers, (a + bi)(c + di) = ac + adi + bci + bdi^2 = (ac - bd) + (ad + bc)i.

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CCSS.HSN.CN.A.2

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What is the result of multiplying (2i)(3i)?

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(2i)(3i) = 6i^2 = 6(-1) = -6.

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CCSS.HSN.CN.A.2

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How do you divide complex numbers?

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To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator: \frac{a + bi}{c + di} = \frac{(a + bi)(c - di)}{c^2 + d^2}.

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CCSS.HSN.CN.A.3

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What is the conjugate of a complex number?

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The conjugate of a complex number a + bi is a - bi.

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CCSS.HSN.CN.A.3

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CCSS.HSN.CN.A.2

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CCSS.HSN.CN.A.2

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CCSS.HSN.CN.A.2