IXL - Absolute values of complex numbers (Algebra 2 practice)

Find the absolute value.

–

𝑖

Simplify all radicals in your answer.

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Learn with an example

question

Find the absolute value.

4𝑖

Simplify all radicals in your answer.

key idea

The absolute value or modulus of a complex number

𝑖

is the distance between the origin and the point

𝑖

in the complex plane.

It can be computed using the distance formula:

𝑖

solution

Since

4𝑖

is a purely imaginary number, its real part is 0.

4𝑖

Absolute value of a complex number

So, the absolute value of

4𝑖

is 4.

You can also find the absolute value geometrically. The point

(

)

represents the number

4𝑖

in the complex plane.

The distance between the origin

(

)

and

(

)

is 4, so

4𝑖

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