Adding and Subtracting 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 the square root of -1. It is used to express complex numbers.

Tags

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

How do you subtract two complex numbers?

Back

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

Tags

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 obtained by changing the sign of the imaginary part.

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CCSS.HSN.CN.A.3

Front

What is the modulus of a complex number?

Back

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

Front

How do you find the sum of (3 + 4i) and (1 + 2i)?

Back

(3 + 4i) + (1 + 2i) = (3 + 1) + (4 + 2)i = 4 + 6i.

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CCSS.HSN.CN.A.2

Front

How do you find the difference of (5 + 3i) and (2 + 7i)?

Back

(5 + 3i) - (2 + 7i) = (5 - 2) + (3 - 7)i = 3 - 4i.

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CCSS.HSN.CN.A.2

Front

What is the real part of the complex number 6 - 2i?

Back

The real part of the complex number 6 - 2i is 6.

Tags

CCSS.HSN.CN.A.1

Front

What is the imaginary part of the complex number 4 + 5i?

Back

The imaginary part of the complex number 4 + 5i is 5.

Tags

CCSS.HSN.CN.A.1