What is the relationship between real numbers and imaginary numbers?

Real numbers are on the number line, while imaginary numbers are on a perpendicular line, forming the complex plane.

What is a complex number?

A complex number is a number that has a real part and an imaginary part, expressed as $$a + bi$$ , where $$a$$ is the real part and $$b$$ is the imaginary part.

How do you add complex numbers?

To add complex numbers, add their real parts and their imaginary parts separately.

How do you multiply complex numbers?

To multiply complex numbers, use the distributive property and apply the fact that $$i^2 = -1$$ .

What is the modulus of a complex number $$a + bi$$ ?

The modulus is given by $$\sqrt{a^2 + b^2}$$ .

Flashcard

•

Mathematics

•

11th Grade

•

Practice Problem

•

Easy

•

CCSS

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

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FLASHCARD QUESTION

Front

What is the value of $\sqrt{-1}$ ?

Back

The value is $i$ , which is the imaginary unit.

Tags

CCSS.HSN.CN.A.1

FLASHCARD QUESTION

Front

What is $i^2$ ?

Back

$i^2 = -1$ .

Tags

CCSS.HSN.CN.A.1

FLASHCARD QUESTION

Front

What is $i^3$ ?

Back

$i^3 = -i$ .

Tags

CCSS.HSN.CN.A.2

FLASHCARD QUESTION

Front

What is $i^4$ ?

Back

$i^4 = 1$ .

Tags

CCSS.HSN.CN.A.2

FLASHCARD QUESTION

Front

What is $i^5$ ?

Back

$i^5 = i$ .

Tags

CCSS.HSN.CN.A.2

FLASHCARD QUESTION

Front

What is $i^6$ ?

Back

$i^6 = -1$ .

Tags

CCSS.HSN.CN.A.2

FLASHCARD QUESTION

Front

What is $i^7$ ?

Back

$i^7 = -i$ .

Tags

CCSS.HSN.CN.A.2

FLASHCARD QUESTION

Front

What is $i^8$ ?

Back

$i^8 = 1$ .

Tags

CCSS.HSN.CN.A.2

FLASHCARD QUESTION

Front

Define imaginary numbers.

Back

Imaginary numbers are numbers that can be written as a real number multiplied by the imaginary unit $i$ .

Tags

CCSS.HSN.CN.A.1

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