Final answer:
The locus of a complex number z, where the imaginary part is -2 and the real part is 1/i, is equivalent to -3i. Therefore, the locus of z is a point on the complex plane at the coordinates (0, -3), which is located on the imaginary axis three units below the origin.
Step-by-step explanation:
If z is a complex number where the imaginary part of z is equal to -2 and the real part of z is equal to 1/i, we first need to determine the value of 1/i. We know that i is the imaginary unit, meaning i equals the square root of -1. To express 1/i in a standard form, we multiply both the numerator and the denominator by i, which gives us i/i2 or i/(-1) which simplifies to -i. The real part of z is therefore -i. Since the imaginary part is -2, z can be expressed as z = -i - 2i or z = -3i.
For a locus of the complex number z = x + yi, we generally define a set of points that satisfy a certain condition. In this case, z will always have an imaginary part of -3 and a real part of 0. Thus, the locus of z is a single point on the complex plane at the coordinates (0, -3), which corresponds to three units below the origin on the imaginary axis.