Which of the following numbers is equal to 5/i?

Rationale

-5i

To find the value of ( frac{5}{i} ), we can multiply the numerator and denominator by ( -i ) to eliminate the imaginary unit in the denominator. This results in ( frac{5 * (-i)}{i * (-i)} = frac{-5i}{1} = -5i ).

A (-5) YOUR ANSWER

This choice represents a real number, while ( frac{5}{i} ) yields an imaginary result. The simplification process shows that multiplying by ( -i ) leads to an imaginary number, confirming that -5 cannot be the answer.

B (5i) YOUR ANSWER

This choice suggests a positive imaginary number. However, the simplification of ( frac{5}{i} ) results in ( -5i ), not ( 5i ). The signs of the imaginary parts must be carefully considered, leading to the conclusion that this option is incorrect.

C (-5i) CORRECT

This option is correct as it directly results from the simplification of ( frac{5}{i} ). By multiplying the numerator and denominator by ( -i), we correctly arrive at ( -5i ), which matches this choice.

D (5) YOUR ANSWER

This is a real number, but dividing by i results in an imaginary value. Since -5/i =−5i, this option does not match and is incorrect.

E (5-i) YOUR ANSWER

This choice combines both real and imaginary parts, suggesting a complex number. However, the simplification of ( frac{5}{i} ) does not yield a result resembling ( 5-i ), as the correct result is purely imaginary.

Conclusion

The expression ( frac{5}{i} ) simplifies to ( -5i ) by rationalizing the denominator. The correct answer is thus option C, while all other choices fail to represent the correct result of this mathematical operation. Understanding the manipulation of complex numbers is essential in arriving at the correct conclusion.

Which of the following numbers is equal to 5/i?

-5i

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