IXL - Distance in the complex plane (Precalculus practice)

Find the complex numbers

and

Then, find the distance between them.

Write complex numbers in the form

𝑖

Simplify all radicals.

distance

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question

Find the complex numbers

and

Then, find the distance between them.

Write complex numbers in the form

𝑖

Simplify all radicals.

distance

key idea

Distance formula in the complex plane

The distance between the complex numbers

𝑖

and

𝑖

in the complex plane is the same as the distance between points

(

)

and

(

)

in the coordinate plane. It is the absolute value or modulus of their difference.

–

(

–

)

(

–

)

𝑖

(

–

)

(

–

)

solution

The complex number

is at (9, 5), so

5𝑖

The complex number

is at (9, 0), so

The distance between

and

is the length of the segment connecting them.

As you can see, the segment connecting

and

has length 5. You can check your answer by using the distance formula.

The distance between

and

in the complex plane is

–

(

5𝑖

)

–

(

–

)

5𝑖

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Not feeling ready yet? These can help:

W.6Absolute value in the complex plane

V.1Add and subtract complex numbers

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