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Ivahew [28]
2 years ago
8

Four complex numbers form the vertices of a square in the complex plane. Three of the numbers are $-19 32i,$ $-5 12i,$ and $-22

15i$. What is the fourth number
Mathematics
1 answer:
Ugo [173]2 years ago
6 0

If the three numbers of a square in the complex plane are -19+32i,-5+12i and -22+15i , then the fourth complex number -2+19i.

Given -19+32i,-5+12i and -22+15i are three numbers.

Complex numbers are those numbers which extends the real numbers with an imaginary i. In this i^{2}=-1. Major complex numbers are in the form a+ bi where a and b are real numbers.

let the fourth complex numbers be x+yi. Then according to question;

=(-22+15i)-(-5+12i)

=(cos π/2+i sin π/2) (x+yi)-(-5+12i)

-17+3i=-y+12+(x+5)i

Now solving for x and y by equating both sides.

x=-2 and y=29

Put the value of x and y in x+yi

Z=-2+29i

Hence if the three numbers which forms vertices of a square are -19+32i,-5+12i,-22+25i then the fourth complex numbers be -2+29i.

Learn more about complex numbers at brainly.com/question/10662770

#SPJ4

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Answer:

g=28, that may not be how the teacher would want you to show your work, but that's how I find the answer!

Step-by-step explanation:

6-3=3

31-3=28

28=g

So therefore 28+6-3=31

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Solve for x and write your answer in simplest form.<br><br> -1/2 -1/2(4/5x+1) = -2 -3x
dimaraw [331]

The solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.

<h3>What is the solution of the equation as described in the task content?</h3>

It follows from the task content that the solution to the equation is to be determined and expressed in its simplest form.

Given;

-1/2 -1/2(4/5x+1) = -2 -3x

By distributing the coefficients: we have;

-1/2 - 2/5x - 1/2 = -2 -3x

Hence, by collecting like terms; we have;

-1/2 - 1/2 + 2 = -3x + (2/5)x

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Therefore; by cross-multiplication; we have;

5 = -13x

Divide both sides by; -13.

x = -5/13.

Ultimately, the solution of the equation which is as described in the task content when expressed in its simplest form is; -5/13.

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