Question

use the following image to answer the question.
question 37
what is the complex number shown on the complex plane below?
select one
3+2i
4+2i
4-2i
3-2i

Explanation:

Step1: Recall complex plane coordinates

In a complex plane, a complex number \(a + bi\) is represented as a point \((a, b)\), where \(a\) is the real part (x - coordinate) and \(b\) is the imaginary part (y - coordinate). If \(b\) is negative, the point is below the real axis (x - axis), and if \(b\) is positive, it is above.

Step2: Analyze the given point

Looking at the graph, the point is in the fourth quadrant (since the y - coordinate is negative). Let's find the x and y coordinates. The x - coordinate (real part) is 4 (since it is 4 units to the right of the origin on the x - axis) and the y - coordinate (imaginary part) is - 2 (since it is 2 units below the x - axis). So the complex number is \(4-2i\). We can also check the other options:

• For \(3 + 2i\), the point would be \((3,2)\) (first quadrant), which does not match.
• For \(4+2i\), the point would be \((4,2)\) (first quadrant), which does not match.
• For \(4 - 2i\), the point is \((4,-2)\), which matches the position of the dot on the complex plane.

Answer:

C. \(4 - 2i\) (assuming the options are labeled as A: \(3 + 2i\), B: \(4+2i\), C: \(4 - 2i\), D: \(3 - 2i\); if the original options have different labels, adjust accordingly. From the given options, the correct one is the third option which is \(4 - 2i\))