Midpoint in the Complex Plane

Section 6.5

Can you do 46 as a guide for me to do the rest on my days off? Thank you.

 

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

 

I will do the rest this weekend. Thanks..

 

correct

 

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

 

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)".

 

Thanks.

 

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?

 

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

 

what is your point?

 

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

 

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

 

Well, wherever it came from, it is still wrong. A complex number has two parts, a "real part" and an "imaginary part". Only the "imaginary part" is multiplied by i.

Either it was wrong on the internet or you copied it incorrectly.