Which point represents the quotient of 3-1?

A
B
C
D

The point that represents the quotient [tex]\frac{3 - i}{i}[/tex] is (C)

The quotient is given as:

[tex]Quotient = \frac{3 - i}{i}[/tex]

Rationalize the expression

[tex]Quotient = \frac{3 - i}{i} \times \frac ii[/tex]

Expand the above expression

[tex]Quotient = \frac{3i - i^2}{i^2}[/tex]

Evaluate all exponents

[tex]Quotient = \frac{3i - (-1)}{-1}[/tex]

Remove bracket

[tex]Quotient = \frac{3i +1}{-1}[/tex]

Rewrite the above expression as follows:

[tex]Quotient = -3i -1[/tex]

Further, rewrite as:

[tex]Quotient = -1-3i[/tex]

In the above expression, the real part is -1, and the imaginary part is -3.

This point is represented by point C, because:

[tex]C = (-1,-3)[/tex]

Hence, the point that represents the quotient [tex]\frac{3 - i}{i}[/tex] is (C)

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