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, defined as the square root of -1.

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CCSS.HSN.CN.A.1

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as i = √(-1). It is used to extend the real number system to include solutions to equations that do not have real solutions.

Tags

CCSS.HSN.CN.A.1

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers (a + bi)(c + di), use the distributive property: ac + adi + bci + bdi². Remember that i² = -1.

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CCSS.HSN.CN.A.2

Front

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

Back

-12 - 6i.

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CCSS.HSN.CN.A.2

Front

What is the result of (2i)(3i)?

Back

-6.

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CCSS.HSN.CN.A.2

Front

How do you find the sum of two complex numbers?

Back

To find the sum of two complex numbers (a + bi) + (c + di), add the real parts and the imaginary parts separately: (a + c) + (b + d)i.

Tags

CCSS.HSN.CN.A.2

Front

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

Back

-2 + 6i.

Tags

CCSS.HSN.CN.A.2

Front

How do you simplify the expression (7 + 2i)(9 - 6i)?

Back

Use the distributive property: (7*9) + (7*-6i) + (2i*9) + (2i*-6i) = 63 - 42i + 18i - 12 = 75 - 24i.

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CCSS.HSN.CN.A.2

Front

What is the result of simplifying (7 + 2i)(9 - 6i)?

Back

75 - 24i.

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CCSS.HSN.CN.A.2

Front

How do you simplify the expression 3i - (4 + 7i)?

Back

Distribute the negative: 3i - 4 - 7i = -4 - 4i.

Tags

CCSS.HSN.CN.A.2