# Midpoint in the Complex Plane

Discussion in 'Geometry and Trigonometry' started by nycmathguy, Feb 16, 2022.

1. ### nycmathguy

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Section 6.5

Can you do 46 as a guide for me to do the rest on my days off? Thank you. nycmathguy, Feb 16, 2022
2. ### MathLover1

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46.
-3+4i
1-2i

The midpoint of the line segment joining two complex numbers a + bi and s + ti is the
average of the numbers at the endpoints.

Midpoint Formula in the Complex Plane is:

Midpoint = (a + s)/2+ ((b + t)/2 )i

-3+4i=a + bi => a=-3, b=4
1-2i= s + ti =>s=1, t=-2

Midpoint = (-3 + 1)/2+ ((4 -2)/2 )i=-1+i

MathLover1, Feb 16, 2022
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3. ### nycmathguy

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I will do the rest this weekend. Thanks..

nycmathguy, Feb 16, 2022
4. ### nycmathguy

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422 nycmathguy, Feb 18, 2022
5. ### MathLover1

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correct

MathLover1, Feb 18, 2022
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6. ### Country Boy

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NO! Given the points, $$-1+ \frac{3}{4}i$$ and

Country Boy, Feb 19, 2022
7. ### Country Boy

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First, you write the general formula as "[(a+ s)/2+ (b+ t)/2]i" which is incorrect. It should be (a+ s)/2+ [(b+ t)/2]i.

Also, didn't you say that these "points in the complex plane" are to be written as "a+ bi", NOT as "(a, b)"? The midpoint of the line segment in the complex plane with endpoints -1- (3/4)i and 1/2+ (1/4)i is -1/4- (1/4)i, not "(-1/4, -1/4)".

Country Boy, Feb 19, 2022
8. ### nycmathguy

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Thanks.

nycmathguy, Feb 19, 2022
9. ### MathLover1

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he was using right formula btw, you say
"he write the general formula as "[(a+ s)/2+ (b+ t)/2]i" which is incorrect. It should be (a+ s)/2+ [(b+ t)/2]i."
what is the difference between your formula and his formula?

MathLover1, Feb 19, 2022
10. ### Country Boy

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2+ 3i is NOT the same as [2+ 3]i= 5i.

Country Boy, Feb 19, 2022
11. ### MathLover1

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MathLover1, Feb 19, 2022
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12. ### Country Boy

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You asked "What is the difference between your formula and his formula?

My point was to answer that question!
His formula was "[(a+ s)/2+ (b+ t)/2]i" which is incorrect. My formula was "(a+ s)/2+ [(b+ t)/2]i." Notice the "[ ]" in his formula- everything inside [ ] is multiplied by i.

In my formula the [ ] surrounds only the '(b+ t)/2' and only that is multiplied by i.

i

Country Boy, Feb 20, 2022
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13. ### nycmathguy

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I found the posted formula online. It did not come out of my ass.

nycmathguy, Feb 21, 2022
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