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 does the imaginary unit 'i' represent?

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CCSS.HSN.CN.A.1

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CCSS.HSN.CN.A.1

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How do you simplify the expression (10 + 15i) - (48 - 30i)?

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The simplified form is -38 + 45i.

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CCSS.HSN.CN.A.2

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The result is 1.

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CCSS.HSN.CN.A.3

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The simplified form is 3 + 2i.

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CCSS.HSN.CN.A.1

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The simplified form is 2 - 3i.

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CCSS.HSN.CN.A.1

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

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

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CCSS.HSN.CN.A.3

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How do you add two complex numbers, such as (3 + 4i) and (1 + 2i)?

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To add complex numbers, combine the real parts and the imaginary parts: (3 + 1) + (4i + 2i) = 4 + 6i.

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CCSS.HSN.CN.A.2