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What is the definition of a complex number?

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A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit.

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CCSS.HSN.CN.A.1

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What does the imaginary unit 'i' represent?

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CCSS.HSN.CN.A.1

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CCSS.HSN.CN.A.1

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How do you add two complex numbers?

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To add two complex numbers, add their real parts and their imaginary parts separately. For example, (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 subtract two complex numbers?

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To subtract two complex numbers, subtract their real parts and their imaginary parts separately. For example, (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 product of two complex numbers (a + bi)(c + di)?

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The product is given by (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 conjugate of a complex number a + bi?

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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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How do you multiply a complex number by its conjugate?

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Multiplying a complex number by its conjugate results in a real number: (a + bi)(a - bi) = a^2 + b^2.

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CCSS.HSN.CN.A.2

Front

What is the modulus of a complex number a + bi?

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CCSS.HSN.CN.A.2