Final answer:
The expression ((5 - 8i) - 2i ((2 - 3i)) simplifies to -1 - 12i, which is the complex number in standard form.
Step-by-step explanation:
To express the given expression (5 - 8i) - 2i (2 - 3i) as a complex number in standard form, we first apply the distributive property to the second term.
(5 - 8i) - 2i(2 - 3i)
We distribute -2i across (2 - 3i):
= (5 - 8i) - (4i + 6)
Next, we combine like terms:
= 5 - 8i - 4i - 6
Combine the real parts (5 and -6) and the imaginary parts (-8i and -4i):
= (5 - 6) + (-8i - 4i)
Simplifying the real and imaginary parts:
= -1 - 12i
The standard form of a complex number is a + bi, where 'a' is the real part and 'bi' is the imaginary part. So, the complex number in standard form is -1 - 12i.