Adding, Subtracting and Multiplying Complex numbers

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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 i² = -1.

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CCSS.HSN.CN.A.1

Front

How do you add two complex numbers?

Back

To add two complex numbers, add their real parts and their 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 two complex numbers?

Back

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

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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 a real number?

Back

To multiply a complex number by a real number, multiply both the real and imaginary parts by that number. For example, k(a + bi) = ka + kbi.

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CCSS.HSN.CN.A.2

Front

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

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The result is 31 + 5i.

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CCSS.HSN.CN.A.2

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What is the result of (-7 + 9i) + (2 - 10i)?

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The result is -5 - i.

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CCSS.HSN.CN.A.2

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

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The result is 12 - 28i.

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CCSS.HSN.CN.C.8

Front

What is the result of (11 - 3i)(2 + i)?

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The result is 25 + 5i.

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CCSS.HSN.CN.A.2