Question

which of the following statements is true about the plot of the expression -1.5+4i A. The point will lie to the right of the vertical axis b. The point will lie below the horizontal axis. The point will lie in quadrant ll of the argand diagram d. The point will lie in quadrant IV of the quadrant argand diagram

Answer 1

To determine where the point corresponding to the expression \(-1.5 + 4i\) lies on the Argand diagram, let's break down the components of the complex number:

• The real part is \(-1.5\).
• The imaginary part is \(4\).

Now, we can analyze the position of this point:

1. The real part \(-1.5\) is negative, which means it lies to the left of the vertical axis (the imaginary axis).
2. The imaginary part \(4\) is positive, which means it lies above the horizontal axis (the real axis).

Given this information, we can conclude the following:

• Since the point has a negative real part and a positive imaginary part, it lies in quadrant II of the Argand diagram.

Now let's evaluate each of the statements:

A. The point will lie to the right of the vertical axis. (False, as it lies to the left due to negative real part)

B. The point will lie below the horizontal axis. (False, as it lies above due to positive imaginary part)

C. The point will lie in quadrant II of the Argand diagram. (True, since it has a negative real part and a positive imaginary part)

D. The point will lie in quadrant IV of the Argand diagram. (False, as it is not in quadrant IV)

Thus, the correct answer is C: The point will lie in quadrant II of the Argand diagram.