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Let z be a complex number satisfying the...

Let `z` be a complex number satisfying the equation `(z^3+3)^2=-16` , then find the value of `|z|`

Text Solution

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The correct Answer is:
`5^(1//3)`
`(z^(3)+ 3)^(2) = 16i^(2)`
`z^(3) + 3 = 4i or - 4i`
`z^(3) = -3 + 4i or - 3 - 4i`
`z^(3) = -3 + 4i or - 3-4i`
`|z^(3)| = |-3+4i| = 5`
`|z|^(3) = 5`
`rArr |z| = 5^(1//3)`
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