What is the relationship between real numbers and imaginary numbers?

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

What is a complex number?

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.

How do you add two complex numbers?

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

How do you multiply two complex numbers?

To multiply two 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

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Mathematics

•

11th Grade

•

Practice Problem

•

Hard

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CCSS

HSN.CN.A.1, HSN.CN.A.2, HSA-REI.B.4B

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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', where i is defined as the square root of -1.

Tags

CCSS.HSN.CN.A.1

FLASHCARD QUESTION

Front

What is the value of $i^2$ ?

Back

$-1$ .

Tags

CCSS.HSN.CN.A.1

FLASHCARD QUESTION

Front

What is the value of $i^3$ ?

Back

$-i$ .

Tags

CCSS.HSN.CN.A.2

FLASHCARD QUESTION

Front

What is the value of $i^4$ ?

Back

$1$ .

Tags

CCSS.HSN.CN.A.2

FLASHCARD QUESTION

Front

What is the value of $i^9$ ?

Back

$i$ .

Tags

CCSS.HSN.CN.A.2

FLASHCARD QUESTION

Front

Solve: $x^2 + 36 = 0$

Back

$x = \pm 6i$ .

Tags

CCSS.HSA-REI.B.4B

CCSS.HSN.CN.C.7

FLASHCARD QUESTION

Front

Simplify: $\sqrt{-4}$

Back

$2i$ .

FLASHCARD QUESTION

Front

Simplify: $\sqrt{-12}$

Back

$2i\sqrt{3}$ .

FLASHCARD QUESTION

Front

What is the definition of the imaginary unit 'i'?

Back

'i' is defined as $\sqrt{-1}$ .

Tags

CCSS.HSN.CN.A.1

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