Dividing Complex Numbers

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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 the square root of -1.

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CCSS.HSN.CN.A.1

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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 obtained by changing the sign of the imaginary part.

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CCSS.HSN.CN.A.3

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How do you multiply complex numbers?

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To multiply complex numbers, use the distributive property (FOIL method) and apply the fact that i^2 = -1.

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CCSS.HSN.CN.A.2

Front

What is the formula for dividing 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

Front

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

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Dividing a complex number by its conjugate results in a real number.

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CCSS.HSN.CN.A.3

Front

What is the significance of the denominator in complex division?

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The denominator must not be zero, and it is often simplified by multiplying by the conjugate to eliminate the imaginary part.

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CCSS.HSN.CN.A.3

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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 simplify the expression \frac{a + bi}{c + di}?

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Multiply the numerator and denominator by the conjugate of the denominator (c - di) to simplify.

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CCSS.HSN.CN.A.3

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What is the real part of the complex number \frac{14}{7-6i}?

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The real part of \frac{14}{7-6i} after simplification is \frac{98}{85}.

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CCSS.HSN.CN.A.3

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What is the imaginary part of the complex number \frac{5}{-1-9i}?

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The imaginary part of \frac{5}{-1-9i} after simplification is \frac{45}{82}.

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CCSS.HSN.CN.A.3