Add 3+ 4i and -4+2i graphically
My class got 1+ 2 radical 10 /2 and 1-2 radical 10 /2 . whenever i put this into the y= graph, nothing shows up on the graph. Can someone tell me how to solve this algebraically and graphically?
add the real and imaginary parts separately:
3+4i + -4+2i = (3-4)+(4+2)i = -1 + 6i
on a graph, draw a line 3 units right, 4 units up to (3,4)
From there, draw a line 14 units left and two up to (-1,6)
To add complex numbers graphically, you can plot them on the complex plane and then find the resultant vector by connecting the two points.
For the given complex numbers:
A = 3 + 4i
B = -4 + 2i
Step 1: Plot Point A on the complex plane. Since A has the real part 3 and the imaginary part 4, you can plot it as a point in the coordinate system on the complex plane.
Step 2: Plot Point B on the complex plane in the same way. Since B has the real part -4 and the imaginary part 2, plot it as a point on the complex plane.
Step 3: Connect Point A and Point B with a vector. This vector represents the addition of the two complex numbers.
Step 4: To find the sum vector, measure the length of the vector connecting Point A and Point B, as well as the angle it makes with the positive real axis.
To solve the given algebraic expression, you have:
x = (1 + 2√10) / 2
y = (1 - 2√10) / 2
To graphically solve this, you can use a graphing calculator or software. Here are the steps to solve it algebraically and graphically using a graphing calculator:
Step 1: In the graphing calculator, open the equation editor or the "Y=" screen.
Step 2: Enter the equations:
Y1 = (1 + 2sqrt(10)) / 2
Y2 = (1 - 2sqrt(10)) / 2
Step 3: Adjust the window settings to include the appropriate x and y ranges.
Step 4: Graph the equations.
If nothing is showing up on the graph, check the window settings to make sure that the range is set correctly. If the range is too small or not set properly, the graph may not be displayed.
Additionally, double-check the entered equations to ensure that they are correct, especially when dealing with radical expressions.
I hope this helps you solve the problem both algebraically and graphically!