Homework Help

what is complex in c where 6complex=conj+7 times -1 power 1/2?

user profile pic

mozostax | Student, Undergraduate | (Level 2) eNoter

Posted January 8, 2013 at 1:13 PM via web

dislike 1 like

what is complex in c where 6complex=conj+7 times -1 power 1/2?

1 Answer | Add Yours

user profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted January 8, 2013 at 1:24 PM (Answer #1)

dislike 1 like

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.`

 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes