Operations with 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 i^2 = -1.

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CCSS.HSN.CN.A.1

Front

What is the imaginary unit 'i'?

Back

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CCSS.HSN.CN.A.1

Front

How do you add complex numbers?

Back

To add 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 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

The product of two complex numbers (a + bi)(c + di) is calculated using the distributive property: ac + adi + bci + bdi^2, which simplifies to (ac - bd) + (ad + bc)i.

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CCSS.HSN.CN.A.2

Front

How do you simplify the expression (5 - 6i) - (6 - 3i)?

Back

The simplified form is -1 - 3i.

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CCSS.HSN.CN.A.2

Front

What is the result of multiplying (-3 + 2i)(1 - 4i)?

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The result is 5 + 14i.

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CCSS.HSN.CN.A.2

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How do you square a complex number?

Back

To square a complex number (a + bi), use the formula (a + bi)^2 = a^2 + 2abi + (bi)^2 = a^2 - b^2 + 2abi.

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CCSS.HSN.CN.C.8

Front

What is the simplified form of (-4 - 8i)^2?

Back

The simplified form is -48 + 64i.

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CCSS.HSN.CN.C.8

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It reflects the complex number across the real axis.

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CCSS.HSN.CN.A.3