Final answer:
The expression equivalent to the given complex number 45 + 2i is d) 45 + 2i, as it possesses the same real and imaginary components. The other options a), b), and c) have different real parts, imaginary parts, or both, and hence are not equivalent.
Step-by-step explanation:
The question asks which expressions are equivalent to a given complex number 45 + 2i. By definition, an equivalent expression to a complex number will have the same real part and the same imaginary part. Therefore, the correct answer is the expression that has the real part as 45 and the imaginary part as 2i.
The answer is:
d) 45 + 2i, as it is identical to the given complex number and therefore has the same value.
- a) 45 - 2i is the complex conjugate of the given complex number and is not equivalent.
- b) 2i - 45 has the real and imaginary parts reversed and a change in sign, so it is not equivalent.
- c) -45 - 2i has both real and imaginary parts with opposite signs, so it is not equivalent.