How Do You Plot Complex Numbers on a Plane?

AI Thread Summary
To plot complex numbers on a plane, the x-axis represents real numbers while the y-axis represents imaginary numbers. For the given numbers, plot them as points using their real and imaginary components; for example, 3-2i is plotted at (3, -2). The axes should be labeled as Re(z) for the real part and Im(z) for the imaginary part. It's important to reference examples in textbooks for clarity on graphing complex numbers. Understanding this foundational concept is crucial as the complexity of working with complex numbers increases.
tg22542
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Homework Statement



Graph the following numbers on a complex plane.

A) 3-2i
B)-4
C)-2+i
D)-3i
D)-1-4i

Can smomeone help me how to get started on this question? I'm not sure what it wants me to do
 
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First, find out what the complex plane looks like. (Hint: it looks just like a regular plane, except the y values are -4i, -3i, ..., 3i, 4i.

Plot A) thru B) from the OP and label the points.

Your work with complex numbers will get MUCH harder from this point.
 
Do you know how to plot (3, -2) on a graph?
 
So use an xaxis of -4i to 4i and a y-axis of -1 to 3 then simply plot them?
 
tg22542 said:

Homework Statement



Graph the following numbers on a complex plane.

A) 3-2i
B)-4
C)-2+i
D)-3i
D)-1-4i

Can smomeone help me how to get started on this question? I'm not sure what it wants me to do

The instructions are pretty clear to me -
Graph the following numbers on a complex plane.
Have you looked in your book? It should have several examples of graphing complex numbers.
 
tg22542 said:
So use an xaxis of -4i to 4i and a y-axis of -1 to 3 then simply plot them?

No, you have your axes the wrong way around. The x-axis corresponds to the real numbers, and the y-axis to the imaginary numbers. To plot a number z = a+ib, you plot (a,b) and you label your real axis (x-axis) as Re(z) and your imaginary axis as Im(z).

Also note that a = a+i0 and ib=0+ib
 
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
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