Practice Magnitude in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Magnitude measures the size or length of a quantity — for a vector (a, b), it is sqrt(a^2 + b^2). For a single number, magnitude is its absolute value: how far it is from zero, ignoring sign or direction.

How big something is, regardless of which way it points—5 miles east and 5 miles west are the same distance.

Showing a random 20 of 50 problems.

Example 1

medium
Solve ∣2x∣=8|2x| = 8.

Example 2

challenge
For which real numbers xx is ∣x∣<3|x| < 3?

Example 3

easy
What is the magnitude of 00?

Example 4

challenge
A complex number has magnitude 1313 and imaginary part 55 with a positive real part. Find the number.

Example 5

easy
Find the magnitude of the vector (−3,−4)(-3, -4).

Example 6

easy
Fill in the blank: the magnitude of any real number is always ____.

Example 7

hard
A hiker walks 33 km left then 55 km right. What is the magnitude of total displacement?

Example 8

medium
Order by magnitude, smallest first: −9,4,−1,6-9, 4, -1, 6.

Example 9

medium
A particle goes 66 km north then 88 km east. Find the magnitude of total displacement.

Example 10

medium
Two displacements: (3,4)(3, 4) then (4,−3)(4, -3). What is the magnitude of the total displacement?

Example 11

challenge
A vector goes (3,4)(3, 4) then (0,−1)(0, -1). What is the magnitude of the total displacement?

Example 12

medium
Compute the distance between −2-2 and 55 on the number line.

Example 13

medium
For which real xx is ∣x∣>3|x| > 3?

Example 14

easy
What is ∣−100∣|-100|?

Example 15

medium
The magnitude of a complex number a+bia+bi is ∣a+bi∣=a2+b2|a+bi|=\sqrt{a^2+b^2}. Find ∣8+6i∣|8 + 6i|.

Example 16

easy
Solve ∣x∣=10|x| = 10.

Example 17

medium
Order by magnitude, smallest first: −12, 5, −8, 3-12,\ 5,\ -8,\ 3.

Example 18

hard
Find ∣7−24i∣|7-24i|.

Example 19

medium
Solve ∣x∣=5|x| = 5 for all real xx.

Example 20

easy
What is the magnitude of the zero vector (0,0)(0, 0)?
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