Alg2CP Complex Numbers Flashcard Review

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What is 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, defined as i = √(-1).

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What is the imaginary unit 'i'?

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The imaginary unit 'i' is defined as the square root of -1, i.e., i = √(-1). It is used to extend the real number system to include solutions to equations that do not have real solutions.

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How do you simplify the square root of a negative number?

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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. It is used to simplify expressions involving complex numbers.

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How do you add complex numbers?

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To add complex numbers, combine the real parts and the imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

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How do you subtract complex numbers?

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To subtract complex numbers, subtract the real parts and the imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

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What is the modulus of a complex number?

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How do you multiply complex numbers?

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To multiply complex numbers, use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2. Remember that i^2 = -1.