Question

plot $-3i$ in the complex plane.

Explanation:

Step1: Recall complex number form

A complex number is \( z = a + bi \), where \( a \) is the real part (\( \text{Re} \)) and \( b \) is the imaginary part (\( \text{Im} \)). For \( -3i \), we can write it as \( 0 + (-3)i \), so \( a = 0 \) (real part) and \( b=-3 \) (imaginary part).

Step2: Locate on complex plane

In the complex plane, the horizontal axis is the real axis (\( \text{Re} \)) and the vertical axis is the imaginary axis (\( \text{Im} \)). To plot \( -3i \), we move 0 units along the real axis (stay at \( x = 0 \)) and move -3 units along the imaginary axis (down 3 units from the origin). So the point is at \( (0, -3) \) in the complex plane (where the first coordinate is real part and the second is imaginary part).

(Note: Since the task is to plot, the key is identifying the coordinates (0, -3) and marking that point on the given grid. The grid has Re (x - axis) and Im (y - axis), so the point is on the Im axis, 3 units below the origin.)

Answer:

To plot \( -3i \) in the complex plane:

• The real part (\( \text{Re} \)) of \( -3i \) (written as \( 0 - 3i \)) is \( 0 \), so we start at the origin (where \( \text{Re}=0 \)).
• The imaginary part (\( \text{Im} \)) is \( -3 \), so we move 3 units down along the imaginary axis (vertical axis).

This places the point at \( (\text{Re}, \text{Im}) = (0, -3) \) on the complex plane (on the imaginary axis, 3 units below the origin).