the complex numbers 1,-1,iorta root3 form which type of triangle in graphical form
assuming "iorta root3" means i√3, then the triangle is equilateral. In fact -1,1,n*i for any real n is isoceles.
To determine which type of triangle is formed by the complex numbers 1, -1, and i√3, we can plot them on the complex plane and examine the side lengths of the resulting triangle.
Let's consider the complex number 1. This corresponds to the point (1, 0) on the complex plane since the real part is 1 and the imaginary part is 0.
Now, let's consider the complex number -1. This corresponds to the point (-1, 0) on the complex plane since the real part is -1 and the imaginary part is 0.
Finally, let's consider the complex number i√3. This corresponds to the point (0, √3) on the complex plane since the real part is 0 and the imaginary part is √3.
If we connect these three points on the complex plane, we get a triangle with side lengths |1-(-1)|, |1-i√3|, and |-1-i√3|. Simplifying these distances, we find that the side lengths of the triangle are:
|1-(-1)| = 2
|1-i√3| = √(1 + (√3)^2) = √(1+3) = 2
|-1-i√3| = √((-1)^2 + (√3)^2) = √(1+3) = 2
Since all three side lengths are equal, we can conclude that the triangle formed by these complex numbers is an equilateral triangle.
In graphical form, the equilateral triangle formed by the complex numbers 1, -1, and i√3 on the complex plane would look something like this:
|i√3
|
|
-------------- (2, 0)
|
|
|-1
I hope this helps! Let me know if you have any further questions.
To determine the type of triangle formed by the complex numbers 1, -1, and i√3 in graphical form, we need to plot these numbers on the complex plane.
The complex plane has two axes, the real axis (x-axis) and the imaginary axis (y-axis). The number 1 lies on the positive x-axis, -1 lies on the negative x-axis, and i√3 lies on the positive y-axis.
Plotting these points, we have:
1: Located at (1, 0)
-1: Located at (-1, 0)
i√3: Located at (0, √3)
Now, connecting these points, we get a triangle. In this case, the triangle formed is an equilateral triangle.
To confirm this, we can measure the lengths of the sides of the triangle using the distance formula. The distance between (1, 0) and (-1, 0) is 2, the distance between (1, 0) and (0, √3) is also 2, and the distance between (-1, 0) and (0, √3) is also 2. Since all three sides are of equal length, the triangle is equilateral.
Therefore, the complex numbers 1, -1, and i√3 form an equilateral triangle in graphical form.