If z = a + bi = (3+i)(2-3i), then z is equal to which of the following?

Rationale

z is equal to (9-7i).

To find the value of z, we need to multiply the complex numbers (3+i) and (2-3i). The calculation results in z = 9 - 7i, confirming that the correct answer is D.

A ((3-7i)) YOUR ANSWER

This choice represents a complex number with a real part of 3 and an imaginary part of -7. However, the multiplication of (3+i) and (2-3i) does not yield this result, as the real part is significantly higher than 3, making this option incorrect.

B ((3+5i)) YOUR ANSWER

This option has a real part of 3 and an imaginary part of 5. The resulting calculation from (3+i)(2-3i) does not match this outcome, as the real part is much larger, thus indicating that this choice is incorrect.

C ((6-6i)) YOUR ANSWER

While this choice presents a complex number with a real part of 6 and an imaginary part of -6, the multiplication of the two complex numbers does not yield this specific result. The calculations show that both parts differ from what is presented here.

D ((9-7i)) CORRECT

This is the correct choice. When we calculate (3+i)(2-3i), we find that it simplifies to 9 - 7i, matching this option exactly.

E ((9+5i)) YOUR ANSWER

This choice has a real part of 9 and an imaginary part of 5. The imaginary part contradicts our calculation, which shows that the imaginary component is -7, not +5, making this option incorrect.

Conclusion

The multiplication of the complex numbers (3+i) and (2-3i) results in the value z = 9 - 7i, confirming that option D is the correct answer. The other choices are incorrect as they do not match the calculated result, highlighting the importance of accurate computation in complex number operations.

If z = a + bi = (3+i)(2-3i), then z is equal to which of the following?

z is equal to (9-7i).

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