Final answer:
To rewrite (8-i)/(3-2i) in standard form a+bi, multiply by the complex conjugate (3+2i)/(3+2i). Simplify to get 2+i, with the real part a equaling 2.
Step-by-step explanation:
The student is asking how to rewrite the complex expression (8 - i) / (3 - 2i) in standard form, which is a + bi, and to determine the value of a. To accomplish this, we should multiply the numerator and the denominator by the complex conjugate of the denominator. The complex conjugate of 3 - 2i is 3 + 2i.
Let's multiply the expression by (3 + 2i)/(3 + 2i):
(8 - i)(3 + 2i) / (3 - 2i)(3 + 2i) = (24 + 16i - 3i - 2i2) / (9 - 6i + 6i - 4i2)
Since i2 = -1:
(24 + 16i - 3i + 2) / (9 + 4)
Simplifying further:
(26 + 13i) / 13 = 2 + i
Therefore, the expression in standard form is 2 + i, and a, the real part, is 2.