Question 5

z is equal to (9-7i)

To find the value of z, we first need to multiply the complex numbers (3+i) and (2-3i). The result of this multiplication is z = 9 - 7i.

A) (3-7i)

This option is incorrect because, while the imaginary part is consistent with the original multiplication, the real part does not match. The real part of the calculated z is 9, not 3.

B) (3+5i)

This option is incorrect as both the real and imaginary parts do not align with the calculated result. The real part is 9 and the imaginary part is -7, not 3 and 5 respectively.

C) (6-6i)

This option is incorrect since both parts do not correspond to the result of the multiplication. The real part should be 9, and the imaginary part should be -7, not 6.

D) (9-7i)

This option is correct as it accurately represents the result of the multiplication of the complex numbers (3+i) and (2-3i). The calculations yield a real part of 9 and an imaginary part of -7.

E) (9+5i)

This option is incorrect because it inaccurately represents the imaginary part of the result. The calculated imaginary part is -7, not +5.

Conclusion

The correct answer is (9-7i) because it is the accurate result of the expression given in the problem. All other options fail to match both the real and imaginary components derived from the multiplication of the complex numbers.