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 - Challenge Me

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

Milo's two robots turn about 0 from 1, one 14 quarter turns and one 23. What is i¹⁴ + i²³ in a + bi form?
Noah adds powers of i on a math club card. What is 3i²¹ − i³⁰ in a + bi form?
Pia simplifies i⁴⁷ + 2i⁵⁰ for the class board. What is i⁴⁷ + 2i⁵⁰ in a + bi form?
Ren marks i¹² and i³¹ on a grid map, then adds them. What is i¹² + i³¹ in a + bi form?
Tala multiplies two puzzle cards: √(-4) × √(-25). What is √(-4) × √(-25)?
Zee works out √(-9) × √(-16) on the board for the class. What is √(-9) × √(-16)?
Esme colors in the steps for 3√(-4) × √(-49). What is 3√(-4) × √(-49)?
Jun's robot reads the card √(-1) × √(-64). What is √(-1) × √(-64)?
Milo raises -2i to the fifth power for a math club puzzle. What is (-2i)⁵?
Noah raises -3i to the fourth power on a grid map. What is (-3i)⁴?

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.

More algebra 2

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