Complex Numbers

Front

What is a complex number?

Back

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

Front

What does the imaginary unit 'i' represent?

Back

The imaginary unit 'i' represents the square root of -1.

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CCSS.HSN.CN.A.1

Front

What is the sum of (5-2i) + (-7+8i)?

Back

-2 + 6i

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CCSS.HSN.CN.A.2

Front

What is the result of 3i + 2i?

Back

5i

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CCSS.HSN.CN.A.2

Front

What does i² equal?

Back

-1

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CCSS.HSN.CN.A.1

Front

What is the result of -6i + 3i?

Back

-3i

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CCSS.HSN.CN.A.2

Front

How do you multiply two complex numbers (a + bi)(c + di)?

Back

(ac - bd) + (ad + bc)i

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CCSS.HSN.CN.A.2

Front

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

Back

The conjugate is a - bi.

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CCSS.HSN.CN.A.3

Front

How do you divide complex numbers (a + bi) / (c + di)?

Back

Multiply the numerator and denominator by the conjugate of the denominator.

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CCSS.HSN.CN.A.3

Front

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

Back

The modulus is √(a² + b²).