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ACT Math : How to graph complex numbers

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Example Questions

Example Question #1 : How To Graph Complex Numbers

The graph of $y=-4x^{2}+6$ passes through (1,2a) in the standard (x,y) coordinate plane. What is the value of ?

Possible Answers:

Correct answer:

Explanation:

To answer this question, we need to correctly identify where to plug in our given values and solve for .

Points on a graph are written in coordinate pairs. These pairs show the value first and the value second. So, for this data:

(1,2a) means that is the value and is the value.

We must now plug in our and values into the original equation and solve. Therefore:

$y=-4x^{2}+6\rightarrow 2a=-4(1)^{2}+6$

We can now begin to solve for by adding up the right side and dividing the entire equation by .

$2a=-4(1)^{2}+6\rightarrow 2a=-4+6\rightarrow2a=2$

$2a=2\rightarrow \frac{2a}{2}=\frac{2}{2}\rightarrow a=1$

Therefore, the value of is .

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Example Question #1 : How To Graph Complex Numbers

Coordinate_pair_1

Point A represents a complex number. Its position is given by which of the following expressions?

Possible Answers:

3-2i

3-2

-2+3

-2+3i

Correct answer:

3-2i

Explanation:

Complex numbers can be represented on the coordinate plane by mapping the real part to the x-axis and the imaginary part to the y-axis. For example, the expression a+bi can be represented graphically by the point (a,b) .

Here, we are given the graph and asked to write the corresponding expression.

3-2i not only correctly identifies the x-coordinate with the real part and the y-coordinate with the imaginary part of the complex number, it also includes the necessary .

3-2 correctly identifies the x-coordinate with the real part and the y-coordinate with the imaginary part of the complex number, but fails to include the necessary .

-2+3i misidentifies the y-coordinate with the real part and the x-coordinate with the imaginary part of the complex number.

-2+3 misidentifies the y-coordinate with the real part and the x-coordinate with the imaginary part of the complex number. It also fails to include the necessary .

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Example Question #1 : How To Graph Complex Numbers

Which of the following graphs represents the expression 4-i ?

Possible Answers:

Complex numbers cannot be represented on a coordinate plane.

Coordinate_pair_3

Coordinate_pair_5

Coordinate_pair_2

Coordinate_pair_4

Correct answer:

Coordinate_pair_4

Explanation:

Here, we are given the complex number 4-i and asked to graph it. We will represent the real part, , on the x-axis, and the imaginary part, , on the y-axis. Note that the coefficient of is ; this is what we will graph on the y-axis. The correct coordinates are (4,-1) .

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Example Question #1 : How To Graph Complex Numbers

The point $\small (3, 5b)$ is on the graph of $\small y=2x^{3}-9$ . What is the value of $\small b$ ?

Possible Answers:

$\small 0$

$\small 45$

$\small 4$

$\small -1$

$\small 9$

Correct answer:

$\small 9$

Explanation:

Because points on a graph are written in the form of $\small (x,y)$ , and the point given was $\small (3, 5b)$ , this means that $\small x=3$ and $\small y=5b$ .

In order to solve for $\small b$ , these values for $\small x$ and $\small y$ must be plugged into the given equation. This gives us the following:

$\small y=2x^3-9$

$\small 5b=2(3)^3-9$

We then solve the equation by finding the value of the right side, then dividing the entire equation by 5, as follows:

$\small 5b=2(27)-9$

5b=54-9

5b=45

$\frac{5b}{5}=\frac{45}{5}$

b=9

Therefore, the value of $\small b$ is $\small 9$ .

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ACT Math : How to graph complex numbers

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Graph Complex Numbers

Example Question #1 : How To Graph Complex Numbers

Example Question #1 : How To Graph Complex Numbers

Example Question #1 : How To Graph Complex Numbers

All ACT Math Resources

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