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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, defined as the square root of -1.

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CCSS.HSN.CN.A.1

Front

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

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CCSS.HSN.CN.A.2

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, subtract the real parts and the imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

Tags

CCSS.HSN.CN.A.2

Front

What is the product of two complex numbers (a + bi)(c + di)?

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The product is given by (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 of a complex number a + bi is a - bi.

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CCSS.HSN.CN.A.3

Front

How do you multiply a complex number by its conjugate?

Back

Multiplying a complex number by its conjugate results in a real number: (a + bi)(a - bi) = a^2 + b^2.

Tags

CCSS.HSN.CN.A.2

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What is the result of (1-3i)(2+5i)?

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The result is 17 - i.

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CCSS.HSN.CN.C.8

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What is the result of (2i + 4)(7i - 3)?

Back

The result is 22i - 26.

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CCSS.HSN.CN.C.8

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

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The sum is -2 + 6i.

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CCSS.HSN.CN.A.2

Front

What is the result of multiplying 2i by (-3i + 7)?

Back

The result is 6 + 14i.

Tags

CCSS.HSN.CN.A.2