Question

think about plotting points in the complex plane to represent the following numbers: -3 + 8i 4i 6 5 - 2i where is each point located on the graph? -3 + 8i is 4i is 6 is 5 - 2i is done

Explanation:

Step1: Recall complex - plane rules

In the complex plane, a complex number $a + bi$ is represented as the point $(a,b)$, where the real part $a$ is the $x$ - coordinate and the imaginary part $b$ is the $y$ - coordinate.

Step2: Locate $-3 + 8i$

For the complex number $-3+8i$, $a=-3$ and $b = 8$. So it is in the second quadrant.

Step3: Locate $4i$

For the complex number $4i=0 + 4i$, $a = 0$ and $b=4$. So it is on the positive $y$ - axis.

Step4: Locate $6$

For the complex number $6=6+0i$, $a = 6$ and $b = 0$. So it is on the positive $x$ - axis.

Step5: Locate $5 - 2i$

For the complex number $5-2i$, $a = 5$ and $b=-2$. So it is in the fourth quadrant.

Answer:

$-3 + 8i$ is in the second quadrant.
$4i$ is on the positive $y$ - axis.
$6$ is on the positive $x$ - axis.
$5 - 2i$ is in the fourth quadrant.