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Question
Show that the equation `z^3 + 2bar(z)` = 0 has five solutions
Solution
Given `z^3 + 2bar(z)` = 0
z3 = `-2 bar(z)`
|z3| = `|- 2| |bar(z)|`
|z|3 = 2|z| .......`[because |"z"| = |bar("z")|]`
|z|3 – 2|z| = 0
|z| [|z|2 – 2] = 0
|z| = 0|z|2 = 2
`"z"bar(z)` = 2
z = `2/bar(z) = +- sqrt(2)` ......`[because bar(z) = (- z^3)/2]`
z = `2/((z^3/-2)`
z4 = 4
It has 4 non zero solutions.
∴ Including z = 0 we have 5 solutions.
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