celesteledesmaa2005 celesteledesmaa2005

12-12-2020
Mathematics

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Which of the following is equivalent to the complex number i^16?

Which of the following is equivalent to the complex number i16 class=

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jimrgrant1 jimrgrant1

12-12-2020

Answer:

A

Step-by-step explanation

i = [tex]\sqrt{-1}[/tex]

i² = ([tex]\sqrt{-1}[/tex] )² = - 1

i³ = i² × i = - 1 × i = - i

[tex]i^{4}[/tex] = i² × i² = - 1 × - 1 = 1 , then

[tex]i^{16}[/tex]

= [tex](i^4)^{4}[/tex]

= [tex](1)^{4}[/tex]

= 1

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