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Express the following in the form `a + i b`(i) `(5+sqrt(2i))/(1-sqrt(2i))` (ii) `i^(-35)`

Text Solution

Verified by Experts

(i)`(5+sqrt2i)/(1-sqrt2i) = (5+sqrt2i)/(1-sqrt2i)**(1+sqrt2i)/(1+sqrt2i)`
`=((5+sqrt2i)(1+sqrt2i))/(1^2+sqrt2^2)`
`=(5+5sqrt2i+sqrt2i+2i^2)/3 = (3+6sqrt2i)/3`
`=1+2sqrt2i`

(ii)`i^-35 = i^(-36+1) = i/i^36 = i/(i^4)^9`
We know, `i^4 = 1`,So,
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