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प्रश्न
Simplify the following and express in the form a + ib:
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
उत्तर
`(3"i"^5 + 2"i"^7 + "i"^9)/("i"^6 + 2"i"^8 + 3"i"^18)`
= `(3("i"^4*"i") + 2("i"^4*"i"^3) + ("i"^4)^2*"i")/("i"^4*"i"^2 + 2("i"^4)^2+ 3("i"^2)^9)`
= `(3(1)* "i" + 2(1)(- "i") + (1)^2 * "i")/((1)(-1) + 2(1)^2 + 3(-1)^9)` ...[∵ i2 = –1, i3 = – i, i4 = 1]
= `(3"i" - 2"i" + "i")/(-1 + 2 - 3)`
= `(2"i")/(-2)`
= – i
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