IXL - Addition in the complex plane (Precalculus practice)

Graph the sum

in the complex plane.

Coordinate plane graph with 4 quadrants, x-axis coordinates from -11 to 11, y-axis coordinates from -11 to 11. The following data are shown. Point (0, -5). Point (0, 10).

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Learn with an example

question

Graph the sum

in the complex plane.

key idea

The complex number

𝑖

is represented by the point

(

)

in the complex plane.

The first coordinate is the real part.
The second coordinate is the imaginary part.

To add complex numbers, add their real parts and add their imaginary parts.

(

𝑖

)

(

𝑖

)

(

)

(

)

𝑖

solution

The complex number

is at (0, 5), so

5𝑖

The complex number

is at (0,

–

𝑖

Their sum is

3𝑖

and has real part equal to 0. So,

is on the imaginary axis, at (0, 3).

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Work it out

Not feeling ready yet? These can help:

V.1Add and subtract complex numbers

Y.6Graph a resultant vector using the parallelogram method

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