Final answer:
To find the standard form of the complex number (2 + 2i)/(1-i), we multiply the numerator and the denominator by the conjugate of the denominator, which results in the number 2i. However, this answer does not match any of the provided options, suggesting a potential error in the question. The correct answer is option d.0 + 2i
Step-by-step explanation:
The standard form of the complex number (2 + 2i)/(1-i) can be found by rationalizing the denominator. To do this, we multiply both the numerator and the denominator by the complex conjugate of the denominator, which is (1+i). The complex conjugate turns the denominator into a real number because when a complex number is multiplied by its conjugate, the imaginary parts cancel out. The multiplication gives us:
(2 + 2i) * (1 + i) / (1 - i) * (1 + i) = (2 + 2i + 2i + 2i^2) / (1 - i^2)
Since i^2 is equal to -1, we get:
(2 + 4i - 2) / (1 + 1) = (4i) / 2 = 2i
However, none of the provided options matches 2i. This suggests there might be an error in the question, or the provided options are incorrect.