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Question
Simplify the following and express in the form a + ib:
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^18)`
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Solution
`(3i^5 + 2i^7 + i^9)/(i^6 + 2i^8 + 3i^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]
= `(3i - 2i + i)/(-1 + 2 - 3)`
= `(2i)/(-2)`
= – i
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