The product (3 + √(- 16))(2 - √(- 25)) is equal to which of the following?

Rationale

Extracting the product yields 26 - 7i.

To simplify the expression (3 + √(-16))(2 - √(-25)), we first calculate the square roots of the negative numbers, leading to complex numbers. The final result of this multiplication simplifies to 26 - 7i.

A (- 14 + 23i) YOUR ANSWER

This choice does not match the simplified product. The calculations for both components do not yield a real part of -14 or an imaginary part of 23i. Instead, it misrepresents the contributions of the square roots involved.

B (-14-7i) YOUR ANSWER

While this option suggests a similar imaginary part, the real part of -14 is incorrect. The proper calculation of the real part should yield 26, not -14. Thus, this option cannot be the result of the multiplication.

C (- 7 + 0i) YOUR ANSWER

This choice implies a real part of -7 and no imaginary part, which is not consistent with the calculated result. Both components of the product should yield positive contributions, making this answer incorrect.

D (5 - i) YOUR ANSWER

This option indicates a real part of 5 and an imaginary part of -1, which diverges significantly from the actual outcome. The calculations show that both the real and imaginary parts are different from those presented here.

E (26-7i) CORRECT

This choice accurately reflects the computed product. The real part is 26, derived from multiplying the real components and adjusting for the imaginary parts. The imaginary part of -7i correctly results from the multiplication of the square roots.

Conclusion

The product of the expression (3 + √(-16))(2 - √(-25)) simplifies to 26 - 7i through careful evaluation of the complex components. Each incorrect choice fails to align with the calculations, highlighting the importance of precise arithmetic in complex number multiplication. The correct answer, E, aptly captures the results of this computation.

The product (3 + √(- 16))(2 - √(- 25)) is equal to which of the following?

Extracting the product yields 26 - 7i.

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