Complex Numbers Operations

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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 = √(-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 the square root of -1, i.e., i = √(-1). It is used to extend the real number system to include solutions to equations that do not have real solutions.

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CCSS.HSN.CN.A.1

Front

How do you add two complex numbers?

Back

To add two 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

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 simplify the expression (3 + 2i) + (4i + 6)?

Back

Combine like terms: (3 + 6) + (2i + 4i) = 9 + 6i.

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CCSS.HSN.CN.A.2

Front

What is the formula for multiplying two complex numbers?

Back

To multiply two complex numbers (a + bi) and (c + di), use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2, and remember that i^2 = -1.

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CCSS.HSN.CN.A.2

Front

What is the result of (5-i)(5-i)?

Back

The result is 24 - 10i.

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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 is used in division and to find the modulus.

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CCSS.HSN.CN.A.3

Front

How do you find the modulus of a complex number?

Back

The modulus of a complex number a + bi is given by |a + bi| = √(a^2 + b^2).

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Back

The result is -1.

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CCSS.HSN.CN.A.2