Question

Which complex number will be plotted below the real axis and to the right of the imaginary axis?

Answer 1

Answer: B) 4 - i

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Explanation:

Any complex number is in the form a+bi which visually can be plotted at the point (a,b). Treat 'a' as 'x', and think of 'b' as 'y'. So (a,b) = (x,y).

a = real part of the number, so because a = x, this means the "real axis" is the x axis.

b = imaginary part of the number, so b = y means the "imaginary axis" is the y axis.

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The statement "below the real axis" indicates the point is below the x axis, so y < 0 and b < 0.

The portion "to the right of the imaginary axis" tells us the point has a positive x coordinate, so x > 0 and a > 0

With a > 0 and b < 0, the only thing that fits is a+bi = 4 + (-1)i = 4-i. In this case, a = 4 and b = -1.

Below is an attached image showing all of the answer choices plotted on the same xy coordinate grid. Only the second answer choice is in the proper region we want.