Multiplying 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 is the real part, b is the imaginary part, and i is the imaginary unit.

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CCSS.HSN.CN.A.1

Front

What does the 'a' represent in a complex number a + bi?

Back

The 'a' represents the real part of the complex number.

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CCSS.HSN.CN.A.1

Front

What does the 'b' represent in a complex number a + bi?

Back

The 'b' represents the imaginary part of the complex number.

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CCSS.HSN.CN.A.1

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1.

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CCSS.HSN.CN.A.1

Front

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

Back

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

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CCSS.HSN.CN.A.2

Front

What is the result of multiplying (5 - i)(5 - i)?

Back

The result is 24 - 10i.

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CCSS.HSN.CN.A.2

Front

What is the result of multiplying (i)(3i)?

Back

The result is -3.

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CCSS.HSN.CN.A.2

Front

How do you simplify the expression 3i(3i - 4)?

Back

The simplified result is -9 - 12i.

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CCSS.HSN.CN.A.2

Front

What is the result of multiplying (-2 + 7i)(4 - 2i)?

Back

The result is 6 + 32i.

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CCSS.HSN.CN.A.2

Front

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

Back

The conjugate of a complex number a + bi is a - bi.

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CCSS.HSN.CN.A.3