7 marks) Let α = −1 + j and β = 4 − j. In each case, solve for z.(a) z − β∗ = Im( α22β + j)(b) z4 = α

Question

7 marks) Let α = −1 + j and β = 4 − j. In each case, solve for z.(a) z − β∗ = Im( α22β + j)(b) z4 = α
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Solution 1

(a) z - β* = Im( α^2/2β + j)

First, let's find the complex conjugate of β, denoted as β*. Since β = 4 - j, β* = 4 + j.

Next, let's calculate α^2/2β. Since α = -1 + j and β = 4 - j, we have:

α^2 = (-1 + j)^2 = 1 - 2j + j^2 = 1 - 2j - 1 = -2j.

So, α^2/2β = -2j/(2*(4 - j)) = -j/(4 - j).

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