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Question
Evaluate: `[i^18 + (1/i)^25]^3`
Solution
`[i^18 + (1/i)^25]^3 = [(i^2)^9 + 1 /((i^2)^12 i)]^3`
= ` [(-1)^9 + 1 /((-1)^12 i)]^3`
= `[ -1 + 1/i xx i/i]^3`
= `[- 1 -i]^3 = - (1 + i)^3`
Now, `[ (a + b)^3 = [a^3 + 3a^2b + 3ab^2 + b^3]`
= - (1 + 3i + 3i2 + i2)
= - (1 + 3i - 3 + i2 .i )
= (- 2 + 3i – i)
= – (- 2 + 2i)
= 2 – 2i
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