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If i z^4+1=0, then prove that z can take...

If `i z^4+1=0,` then prove that `z` can take the value `cospi//8+is inpi//8.`

Text Solution

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`iz^(4) = -1`
`z^(4) = (-1)/(i)`
`or z^(4) =i`
`or z = (i) ^(1//4)`
`or z = (0+i)^(1//4)`
` or z=(0+i)^(1//4)`
`or z = (cos.(pi)/(2) + isin.(pi)/(2))^(1//4) = cos.(pi)/(8)+isin.(pi)/(8)`
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