Grade 11 · Math · Algebra 2

11th grade The imaginary unit i, and its powers worksheet

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The imaginary unit i, and its powers

Grade 11 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

Kira's robot makes 30 quarter turns about 0, starting at 1. Each turn is one factor of i. What is i³⁰?
Luz programs the robot for 51 quarter turns about 0, starting at 1. What is i⁵¹?
Milo needs i⁴⁵ for a math club puzzle. Each factor of i is a quarter turn about 0, starting at 1. What is i⁴⁵?
4.
Pia simplifies √(-50) for a math club card. Which is √(-50) in simplest form?
- 5i√2
- -5i√2
- -5√2
- 5√2
5.
Ren writes √(-12) on the board. Which is √(-12) in simplest form?
- -2√3
- -2i√3
- 2i√3
- 2√3
6.
Zee simplifies √(-72). Which is √(-72) in simplest form?
- -6√2
- 6√2
- 6i√2
- -6i√2
Esme squares 5i on the complex plane. The point moves farther out and turns. What is (5i)²?
Jun's robot starts at 2i and is cubed, so its distance from 0 grows and it turns. What is (2i)³?
Kira writes (3i)³ on a puzzle card. What is (3i)³?
Luz cubes 4i on a grid map. What is (4i)³?

11th grade The imaginary unit i, and its powers worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

The imaginary unit i, and its powers. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can write the square root of a negative number with i.
I can find any power of i by counting quarter turns, using the remainder after dividing by 4.
I can multiply roots of negative numbers by writing each one with i first.

Standard: N-CN.A.1

Words to know

i: The number one step up from 0; i × i = -1.

imaginary axis: The up-and-down line through 0 on the complex plane.

real axis: The across line through 0; ordinary numbers sit here.

quarter turn: A turn about 0 by one corner, counterclockwise, like i × 1 = i.

a + bi form: a across and b up: the real part, then the i part.

remainder: What is left after taking out whole groups of 4.

Common mistakes

Your child turned the minus under a square root into a minus sign (√(-16) written as -4).

Your child took the square root of a negative number and left out the i.

Your child wrote the i but also kept a minus sign in front (√(-16) written as -4i).

What to say

Ask: what number times itself gives -16?

Ask: what does the minus under the root turn into?

Ask: is √(-16) above 0 or below it on the plane?

Questions parents ask

What is the most common mistake with the imaginary unit i, and its powers?

Your child turned the minus under a square root into a minus sign (√(-16) written as -4).

How can I help my child with the imaginary unit i, and its powers?

Ask: what number times itself gives -16?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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