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what is complex in c where 6complex=conj+7 times -1 power 1/2?
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The question is vague, hence, supposing that you need to find the complex number z, that makes the equation `6z=bar z +` `7*(-1)^(1/2)` to hold, you need to perform the following steps.
The first step is to consder the algebraic form of the complex number, such that:
`z = x + i*y`
Hence, its conjugate is `bar z = x - i*y`
Using the complex number theory yields that `sqrt(-1) = i` , hence, substituting ` i` for `(-1)^(1/2)` yields:
`6z=bar z + 7*i`
Substituting `x + i*y` for `z` and `x - i*y` for `bar z` yields:
`6(x + i*y) = x + i*y + 7i`
`6x + 6i*y - x - i(y + 7) = 0`
`5x + i(6y - y - 7) = 0 `
`5x + i(5y - 7) = 0`
Equating the real parts yields:
`5x = 0 => x = 0`
Equating the imaginary parts yields:
`5y - 7 = 0 => 5y = 7 => y = 7/5`
Hence, evaluating the complex number z, under the given conditions, yields `z = (7/5)i.`
Posted by sciencesolve on January 8, 2013 at 1:24 PM (Answer #1)
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