### About Distance and Midpoint Formulas Complex Plane:

We can find the distance between any two complex numbers by modifying our known distance formula to include the difference in real values in the place of the difference in x-values and the difference in imaginary values in the place of the difference in y-values. Additionally, we need to know how to find the midpoint of a line segment in which the endpoints are two complex numbers. To find the midpoint, we will find the average of the real values and the average of the imaginary values for our two given endpoints.

Test Objectives

- Demonstrate an understanding of the complex plane
- Demonstrate an understanding of the distance formula
- Demonstrate the ability to find the distance between two complex numbers
- Demonstrate the ability to find the midpoint of a line segment on the complex plane

#1:

Instructions: find the distance between Z and W.

a)

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#2:

Instructions: find the distance between Z and W.

a)

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#3:

Instructions: find the distance between Z and W.

a)

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#4:

Instructions: find the midpoint of ZW.

a)

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#5:

Instructions: find the midpoint of ZW.

a)

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Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}5$$

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#2:

Solutions:

$$a)\hspace{.2em}2 \sqrt{17}$$

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#3:

Solutions:

$$a)\hspace{.2em}13$$

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#4:

Solutions:

$$a)\hspace{.2em}\frac{5}{2}+ \frac{3}{2}i$$

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#5:

Solutions:

$$a)\hspace{.2em}-1 + i$$