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 represent the square root of negative numbers.

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CCSS.HSN.CN.A.1

Front

How do you add complex numbers?

Back

To add complex numbers, combine 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 result of (5-2i) + (-7+8i)?

Back

The result is -2 + 6i.

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CCSS.HSN.CN.A.2

Front

How do you subtract complex numbers?

Back

To subtract 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?

Back

To multiply complex numbers, use the distributive property (FOIL method). For example, (a + bi)(c + di) = ac + adi + bci + bdi², and since i² = -1, simplify accordingly.

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CCSS.HSN.CN.A.2

Front

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

Back

The result is -34 + 13i.

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CCSS.HSN.CN.C.8

Front

What is the square of the imaginary unit 'i'?

Back

The square of the imaginary unit 'i' is i² = -1.

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CCSS.HSN.CN.A.1

Front

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

Back

The result is -6.

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CCSS.HSN.CN.A.2

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used in division and to find the modulus.

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CCSS.HSN.CN.A.3