Imaginary & Complex Numbers

Front

What is an imaginary number?

Back

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as the square root of -1.

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CCSS.HSN.CN.A.1

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.

Tags

CCSS.HSN.CN.A.1

Front

How do you add two complex numbers?

Back

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

Tags

CCSS.HSN.CN.A.2

Front

What is the result of (10 + 15i) - (48 - 30i)?

Back

The result is -38 + 45i.

Tags

CCSS.HSN.CN.A.2

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers, use the distributive property (FOIL method). For example, (a + bi)(c + di) = ac + adi + bci + bdi^2, and since i^2 = -1, combine like terms.

Tags

CCSS.HSN.CN.A.2

Front

What is the product of (1 - 2i)(6 + 5i)?

Back

The product is 16 - 7i.

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CCSS.HSN.CN.C.8

Front

What is the square root of -4?

Back

The square root of -4 is 2i.

Front

How do you simplify the expression (1 - 2i) + (-4 + 2i)?

Back

To simplify, combine the real parts and the imaginary parts: (1 - 4) + (-2i + 2i) = -3.

Tags

CCSS.HSN.CN.A.2

Front

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

Back

The result is -i + 11.

Tags

CCSS.HSN.CN.A.2