Let's analyze the given problem carefully.
To determine what 86 represents in the context of complex numbers, consider the possibility that 86 may correlate with a value derived from a mathematical concept or formula.
Upon closer examination, 86 can be interpreted as an instruction to consider Euler's formula, [tex]\( e^{i\pi} \)[/tex], which states:
[tex]\[ e^{i\pi} = -1 \][/tex]
Euler's formula is a key relationship in complex numbers and relates the exponential function with the trigonometric functions cosine and sine. Specifically, for [tex]\( \theta = \pi \)[/tex],
[tex]\[ e^{i\pi} = \cos(\pi) + i\sin(\pi) \][/tex]
We know that:
[tex]\[ \cos(\pi) = -1 \][/tex]
[tex]\[ \sin(\pi) = 0 \][/tex]
Thus, substituting these values into Euler's formula, we have:
[tex]\[ e^{i\pi} = -1 + 0i \][/tex]
[tex]\[ e^{i\pi} = -1 \][/tex]
Therefore, 86 represents [tex]\( e^{i\pi} \)[/tex], which simplifies to -1.
So, the correct answer is:
D. -1
