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Explain the pattern in the simplification of imaginary numbersi, i, i, i*,Edit View Insert Format Tools Table12ptParagraph ✓ BIUA Qv T²v**

Explain the pattern in the simplification of imaginary numbersi, i, i, i*,Edit View-example-1

1 Answer

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Given:


i^2,i^2,i^3,i^^4,...

Required:

We need to explain the pattern

Step-by-step explanation:


\begin{gathered} i^1=i \\ i^2=-1 \\ i^3=-i \\ i^4=1 \\ i^5=i^4*i=1*i=i \\ i^6=i^4*i^2=1*-1=-1 \\ i^7=i^4*i^3=1*-i=-i \\ i^8=i^4*i^4=1*1=1 \\ . \\ . \\ . \end{gathered}

As we can see that

the values of


i^(4n+1)

are equal where n is set of real numbers

similarly for


i^(4n+2)

also for


i^(4n+3)

and for


i^(4n+4)

where all n are from the set of real numbers

User Karthikeyan Bose
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