Imaginary and Complex Numbers

Imaginary and Complex Numbers

Assessment

Flashcard

Mathematics

10th - 12th Grade

Practice Problem

Hard

CCSS
HSN.CN.A.1, HSN.CN.A.2, HSN.CN.A.3

+2

Standards-aligned

Created by

Wayground Content

FREE Resource

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of an imaginary number?

Back

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as the square root of -1.

Tags

CCSS.HSN.CN.A.1

2.

FLASHCARD QUESTION

Front

How do you simplify the square root of a negative number, such as √-45?

Back

To simplify √-45, factor out the negative: √-45 = √(45) * √(-1) = √(45) * i = 3i√5.

3.

FLASHCARD QUESTION

Front

What is the result of subtracting two complex numbers, such as (10 + 15i) - (48 - 30i)?

Back

To subtract complex numbers, subtract the real parts and the imaginary parts separately: (10 - 48) + (15i + 30i) = -38 + 45i.

Tags

CCSS.HSN.CN.A.2

4.

FLASHCARD QUESTION

Front

How do you find the sum of two complex numbers, for example, (5 - 2i) + (-7 + 8i)?

Back

To find the sum, add the real parts and the imaginary parts: (5 - 7) + (-2i + 8i) = -2 + 6i.

Tags

CCSS.7.NS.A.1C

5.

FLASHCARD QUESTION

Front

What is the formula for multiplying two complex numbers, such as (4 – 3i)(-7 – 2i)?

Back

Use the distributive property (FOIL): (4)(-7) + (4)(-2i) + (-3i)(-7) + (-3i)(-2i) = -28 - 8i + 21i + 6 = -34 + 13i.

Tags

CCSS.HSN.CN.A.2

6.

FLASHCARD QUESTION

Front

What is the imaginary unit 'i' and what is its significance in complex numbers?

Back

The imaginary unit 'i' is defined as √-1. It allows for the extension of real numbers to complex numbers, which are of the form a + bi, where a and b are real numbers.

Tags

CCSS.HSN.CN.A.1

7.

FLASHCARD QUESTION

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a is the real part and b is the imaginary part.

Tags

CCSS.HSN.CN.A.1

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