If a = 2 + 3i and b = 3 - 2i then a b is equal to which of the following?

Rationale

ab is equal to 5 + i.

To find the product of the complex numbers ( a = 2 + 3i ) and ( b = 3 - 2i ), we apply the distributive property (FOIL method), resulting in ( ab = (2)(3) + (2)(-2i) + (3i)(3) + (3i)(-2i) ). This simplifies to ( 6 - 4i + 9i + 6 = 5 + i ).

A (0) YOUR ANSWER

The product of two non-zero complex numbers cannot be zero unless one of the factors is zero, which is not the case here. Both ( a ) and ( b) are non-zero complex numbers, so this choice is incorrect.

B (- 1 + 5i) YOUR ANSWER

This choice does not match the calculated product. The correct calculation yields ( 5 + i ), and therefore this option does not satisfy the equation of the product ( ab ).

C (1+i) YOUR ANSWER

While this is a complex number, it does not match the result of the product calculation. The computed product ( 5 + i ) is significantly different from ( 1 + i ), making this choice invalid.

D (5 + i) CORRECT

This option is the correct product of the multiplication of the complex numbers ( a ) and ( b ). The calculations confirm that ( ab = (2 + 3i)(3 - 2i) = 5 + i ).

E (5 + 5!) YOUR ANSWER

This choice introduces an unnecessary factorial term which complicates the expression and does not relate to the product of the two complex numbers. The factorial has no relevance in the context of multiplying ( a ) and ( b ).

Conclusion

The product of the complex numbers ( a = 2 + 3i ) and ( b = 3 - 2i ) is successfully calculated as ( 5 + i ). All other options provided either simplify incorrectly or introduce unrelated terms, demonstrating that ( 5 + i ) is the only valid choice. This emphasizes the importance of careful computation in complex multiplication.

If a = 2 + 3i and b = 3 - 2i then a b is equal to which of the following?

ab is equal to 5 + i.

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