Complex Conjugates

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What are complex conjugates?

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Complex conjugates are pairs of complex numbers of the form a + bi and a - bi, where a and b are real numbers.

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CCSS.HSN.CN.A.3

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How do you simplify a complex number?

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To simplify a complex number, combine like terms and express it in the form a + bi.

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CCSS.HSN.CN.A.1

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What is the result of multiplying a complex number by its conjugate?

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The result is a real number: (a + bi)(a - bi) = a^2 + b^2.

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CCSS.HSN.CN.C.8

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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.

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CCSS.HSN.CN.A.1

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How do you add complex numbers?

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To add complex numbers, add their real parts and their imaginary parts separately.

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CCSS.7.NS.A.1C

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How do you subtract complex numbers?

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To subtract complex numbers, subtract their real parts and their imaginary parts separately.

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CCSS.HSN.CN.A.2

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What is the standard form of a complex number?

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The standard form of a complex number is a + bi, where a is the real part and b is the imaginary part.

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CCSS.HSN.CN.A.1

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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.

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CCSS.HSN.CN.A.3

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What is the modulus of a complex number?

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The modulus of a complex number a + bi is given by √(a² + b²).

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What is the argument of a complex number?

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The argument of a complex number a + bi is the angle θ in polar coordinates, calculated as θ = arctan(b/a).