Grade 11 · Math · Algebra 2

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

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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The imaginary unit i, and its powers

Grade 11 Math Worksheet - Building Confidence

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

Esme sorts puzzle cards for math club. One card says √(-49). What is √(-49) written with i?
Jun copies √(-81) onto the board. What is √(-81) written with i?
Kira finds √(-121) on a math club card. What is √(-121) written with i?
Luz marks √(-64) on a grid map of the complex plane. What is √(-64) written with i?
Pia draws quarter turns about 0, starting at 1, one turn for each factor of i. What is i⁵?
Ren traces quarter turns about 0 on the complex plane, starting at 1, one for each factor of i. What is i⁷?
Tala rewrites a puzzle card, 3 + √(-16), as one point on the complex plane. What is 3 + √(-16) in a + bi form?
Zee plots -5 + √(-36) on a grid map. What is -5 + √(-36) in a + bi form?
Esme simplifies 2 − √(-25) for the class board. What is 2 − √(-25) in a + bi form?
Jun colors the point for -1 − √(-9) on a big poster. What is -1 − √(-9) in a + bi form?

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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