How do you simplify $$i^n$$ for any integer n?

Divide n by 4 and use the remainder to find the equivalent power of 'i'.

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Math

Algebra

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Imaginary Numbers Simplifying The Powers Of I

Imaginary Numbers-Simplifying the Powers of i

Flashcard

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSN.CN.A.2, HSN.CN.A.1, HSN.CN.C.8

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15 questions

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FLASHCARD QUESTION

Front

What is 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

FLASHCARD QUESTION

Front

What is the value of $i^2$ ?

Back

$-1$ .

Tags

CCSS.HSN.CN.A.1

FLASHCARD QUESTION

Front

What is the product of two imaginary numbers, (2i)(3i)?

Back

$-6$ .

Tags

CCSS.HSN.CN.A.2

FLASHCARD QUESTION

Front

Simplify $(-3i)^2$ .

Back

$-9$ .

Tags

CCSS.HSN.CN.C.8

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 pattern in the powers of 'i'?

Back

The powers of 'i' cycle every four: $i^1 = i$ , $i^2 = -1$ , $i^3 = -i$ , $i^4 = 1$ .

Tags

CCSS.HSN.CN.A.2

FLASHCARD QUESTION

Front

What is $i^5$ equal to?

Back

$i$ .

Tags

CCSS.HSN.CN.A.2

FLASHCARD QUESTION

Front

What is the result of $i^6$ ?

Back

$-1$ .

Tags

CCSS.HSN.CN.A.2

10.

FLASHCARD QUESTION

Front

What is the result of $i^7$ ?

Back

$-i$ .

Tags

CCSS.HSN.CN.A.2

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