W2 #5 Adding and Subtracting Complex Numbers

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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 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 the square root of -1. It is used to extend the real number system to include solutions to equations that do not have real solutions.

Tags

CCSS.HSN.CN.A.1

Front

How do you add complex numbers?

Back

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

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CCSS.HSN.CN.A.2

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What is the result of (3 + 4i) + (2 + 5i)?

Back

The result is (3 + 2) + (4 + 5)i = 5 + 9i.

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CCSS.HSN.CN.A.2

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

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The result is (7 - 4) + (2 - 3)i = 3 - i.

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CCSS.HSN.CN.A.2

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What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.

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CCSS.HSN.CN.A.3

Front

How do you multiply complex numbers?

Back

To multiply 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.

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CCSS.HSN.CN.A.2

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

Back

The result is (1*3) + (1*4i) + (2i*3) + (2i*4i) = 3 + 4i + 6i - 8 = -5 + 10i.

Tags

CCSS.HSN.CN.A.2

Front

What is the modulus of a complex number?

Back

The modulus of a complex number a + bi is given by √(a² + b²). It represents the distance from the origin to the point (a, b) in the complex plane.