Maharashtra State BoardHSC Science (Electronics) 11th
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Find the value of i6+i7+i8+i9i2+i3 - Mathematics and Statistics

Sum

Find the value of `("i"^6 + "i"^7 + "i"^8 + "i"^9)/("i"^2 + "i"^3)`

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Solution

`("i"^6 + "i"^7 + "i"^8 + "i"^9)/("i"^2 + "i"^3)`

= `("i"^6(1 + "i" + "i"^2 + "i"^3))/("i"^2(1 + "i"))`

= `("i"^4(1 + "i" - 1 - "i"))/(1 + "i")` ...[∵ i2 = – 1 and i3 = – i]

= `("i"^4(0))/(1 + "i")`

= 0.

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