Grade 11 · Math · Precalculus

11th grade Complex numbers in polar form worksheet

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Complex numbers in polar form

Grade 11 Math Worksheet - Building Confidence

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A drone's spot from home, in km, is z = 3 + 4i. Esme plots it on the complex plane. What is |z|, its distance from 0?
A boat's spot from the dock, in km, is z = -5 + 12i. Jun plots it on the complex plane. What is |z|, its distance from 0?
A robot's spot from its charger, in m, is z = 6 − 8i. Kira plots it on the complex plane. What is |z|, its distance from 0?
A kite's spot from the launch point, in m, is z = -8 − 15i. Luz plots it on the complex plane. What is |z|, its distance from 0?
Milo plots z = 4 + 4i at the point (4, 4) on the complex plane. What is its argument θ, from 0° up to 360°?
Noah plots z = -2i at the point (0, -2) on the complex plane. What is its argument θ, from 0° up to 360°?
Tala plots z = -3 + 3i at the point (-3, 3) on the complex plane. What is its argument θ, from 0° up to 360°?
8.
Esme writes z = 2 + 2i in polar form, r(cos θ + i sin θ), with θ from 0° up to 360°. Which is the polar form of 2 + 2i?
- 4(cos 45° + i sin 45°)
- 2√2(cos 315° + i sin 315°)
- 2√2(cos 45° + i sin 45°)
- 8(cos 45° + i sin 45°)
9.
Jun writes z = -4 in polar form, r(cos θ + i sin θ), with θ from 0° up to 360°. Which is the polar form of -4?
- 4(cos 270° + i sin 270°)
- 16(cos 180° + i sin 180°)
- 4(cos 180° + i sin 180°)
10.
Kira writes z = -3 + 3i in polar form, r(cos θ + i sin θ), with θ from 0° up to 360°. Which is the polar form of -3 + 3i?
- 3√2(cos 315° + i sin 315°)
- 3√2(cos 225° + i sin 225°)
- 3√2(cos 135° + i sin 135°)
- 6(cos 135° + i sin 135°)

11th grade Complex numbers in polar form worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Complex numbers in polar form. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find the modulus r and the argument θ of a + bi in any quadrant.
I can write a + bi as r(cos θ + i sin θ), and back, with exact values.
I can read a position given in polar form as east and north parts.

Standard: N-CN.B.4 (+)

Words to know

argument θ: The angle from the positive real axis to z, turning counterclockwise.

polar form: z written as r(cos θ + i sin θ).

reference angle: The angle between z and the nearest part of the real axis.

radian: An angle unit: a full turn is 2π radians.

Common mistakes

Added the real and imaginary parts to get the distance from 0. The distance is the long side of a right triangle, so use a² + b² and a square root.

Stopped at a² + b² and gave r² instead of r.

Turned clockwise to find the angle. Angles on the complex plane turn counterclockwise from the positive real axis.

What to say

Ask: did you take the square root at the end?

Questions parents ask

What is the most common mistake with complex numbers in polar form?

Added the real and imaginary parts to get the distance from 0. The distance is the long side of a right triangle, so use a² + b² and a square root.

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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