IXL - Absolute values of complex numbers (Precalculus practice)

Find the absolute value.

–

𝑖

Simplify all radicals in your answer.

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question

Find the absolute value.

–

𝑖

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

–

𝑖

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

–

𝑖

–

7𝑖

Absolute value of a complex number

(

–

)

Absolute value of a complex number

So, the absolute value of

–

𝑖

is 7.

You can also find the absolute value geometrically. The point

(

–

)

represents the number

–

𝑖

in the complex plane.

The distance between the origin

(

)

and

(

–

)

is 7, so

–

𝑖

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W.6Absolute value in the complex plane

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