Answer:
D. -i
Step-by-step explanation:
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The required value of the complex number [tex]i^{31}[/tex] = -i.
Given that,
To determine the value of complex numbers [tex]i^{31}[/tex].
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
The number that are constitute of real and imaginary numbers are called complex number. complex number can be represents as z = a+ ib ,where a = real part and bi = imaginary part.
Here,
[tex]i^4 = 1[/tex] and [tex]i^3 = -i[/tex]
For complex numbers [tex]i^{31}[/tex]
[tex]=i^{31}\\=(i^4)^7.i^3\\=1.-i\\=-i[/tex]
Thus, the required value of the complex number [tex]i^{31}[/tex] = -i.
Learn more about complex numbers here: https://brainly.com/question/28007020
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