Final answer:
To find the standard form of 1 / (3 - √-4), we multiply by the conjugate to get 3/13 + 2/13i, which means the standard form is A. 3/13 + 2/13i.
Step-by-step explanation:
The student's question asks for the standard form of the complex number 1 / (3 - √-4). To find the standard form, we need to eliminate the imaginary number in the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator, which is 3 + √-4. The √-4 can be written as 2i since √-4 equals 2 multiplied by √-1 and √-1 is defined as i, the imaginary unit.
We thus have:
1 / (3 - 2i) * (3 + 2i)/(3 + 2i) = (3 + 2i)/(3² - (2i)²). Squaring 3 gives us 9, and squaring -2i gives us -4 (since i² = -1), so the denominator becomes 9 - (-4) = 9 + 4 = 13. Expanding the numerator gives us 3 + 2i. Dividing each term by 13 gives us the standard form which is 3/13 + 2/13i. Therefore, the correct answer is A. 3/13 + 2/13i.