Question 35

-5i

To find the value of 5/i, we can multiply the numerator and the denominator by the conjugate of the denominator, which is -i. This results in 5i/-1, simplifying to -5i.

A) -5

This option is incorrect because -5 does not represent the result of the calculation 5/i. The result of this expression involves the imaginary unit, which cannot yield a purely real number like -5.

B) 5i

This option is also incorrect. While 5i is related to the calculation, it represents the numerator before division and does not reflect the final result of the expression 5/i, which simplifies to -5i.

C) -5i

This option is correct. By multiplying both the numerator and denominator of 5/i by -i, we obtain 5i/-1, which simplifies to -5i. Thus, this option accurately represents the value of the expression.

D) 5

This option is incorrect because it is a real number and does not account for the imaginary component resulting from the division by i. The expression 5/i involves an imaginary unit, leading to a different outcome than 5.

E) 5-i

This option is also incorrect. The expression 5/i does not simplify to 5-i. Instead, it results in -5i, which does not include the real part of the number as presented in this option.

Conclusion

The correct answer is -5i, as it derives directly from simplifying the expression 5/i using the conjugate method. All other options either misrepresent the nature of the calculation or yield results that do not align with the outcome of the expression involving the imaginary unit.