Imaginary Numbers

Front

What is an imaginary number?

Back

An imaginary number is a complex 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 the value of i squared (i^2)?

Back

i^2 = -1.

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CCSS.HSN.CN.A.1

Front

What is the value of i cubed (i^3)?

Back

i^3 = -i.

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CCSS.HSN.CN.A.2

Front

What is the value of i to the fourth power (i^4)?

Back

i^4 = 1.

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CCSS.HSN.CN.A.2

Front

How do you express a complex number?

Back

A complex number is expressed in the form a + bi, where a is the real part and b is the imaginary part.

Tags

CCSS.HSN.CN.A.1

Front

What are the real and imaginary parts of the complex number 3.5 - 2.7i?

Back

Real part (Re) = 3.5, Imaginary part (Im) = -2.7.

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CCSS.HSN.CN.A.1

Front

What is the conjugate of a complex number?

Back

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

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CCSS.HSN.CN.A.3

Front

Find the conjugate of the complex number 5 + 7i.

Back

The conjugate is 5 - 7i.

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CCSS.HSN.CN.A.3

Front

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

Back

The result is (a + c) + (b + d)i.

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CCSS.HSN.CN.A.2

Front

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

Back

The result is (ac - bd) + (ad + bc)i.

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CCSS.HSN.CN.A.2