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Calculate: x^2+yi=2+y+2/i+xi

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alexa0048 | Student, Grade 11 | (Level 3) eNoter

Posted April 8, 2013 at 1:34 PM via web

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Calculate:

x^2+yi=2+y+2/i+xi

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sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted April 8, 2013 at 3:13 PM (Answer #1)

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The request of the problem is vague, hence, supposing that you need to evaluate x and y, you need to re-arrange the term to the right, such that:

`x^2 + y*i = 2 + y + 2/i + x*i => x^2*i + y*i*i = 2*i + y*i + 2 + x*i^2` Replacing -1 for `i^2` yields:

`x^2*i + y*(-1) = 2i + y*i + 2 + x*(-1)`

`x^2*i - y = 2i + y*i + 2 - x`

Equating the corresponding parts yields:

`{(x^2 = 2 + y),(-y = 2 - x):} => {(x^2 = 2 + x - 2),(y = x - 2):} `

`{(x^2 = x),(y = x - 2):} => {(x^2 - x = 0),(y = x - 2):} => {(x(x - 1) = 0),(y = x - 2):} => {(x = 0,x = 1),(y =- 2, y = -1):}` Hence, evaluate x and y, under the given conditions, yields `x = 0` and `y = -2` or `x = 1` and `y = -1.`

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