Question

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

Answer 1

Given:

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