in the standard form a + bi, multiply the numerator and denominator of
8−i
3−2i
by the conjugate, 3+2i.This gives
8−i
3−2i
(
3+2i
3+2i
)=
24+16i−3i+(−i)(2i)
32−(2i)2
.Since i2=−1, this last fraction can be rewritten as
24+16i−3i+2
9−(−4)
=
26+13i
13
which simplifies to 2 + i.Therefore, when
8−i
3−2i
is rewritten in the standard form a+bi, the value of a is 2. Choices B, C, and D are incorrect and may be the result of errors in symbolic manipulation. For example, choice B could be the result of mistakenly rewriting 8−i3−2i as