21/z/ =0 or 1, when /z/ = 1, z is fifth root of unity, when /z/ =0 , z=0 :)
$\hspace{-16}\textbf{(1)\;Solve the equation z^4=\bar{z}}:$\\\\ $\textbf{(2)\;If Z\in\mathbb{C}\textbf{\;and $\mid z\mid<\frac{1}{2}.$ Then Show that }}$\\\\ \mathbf{\mid (1+i).z^3+iz\mid<\frac{3}{4} }
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4 Answers
106z=eiθ
=> e4iθ = e-iθ
=> cos(4θ) = cosθ and sin(4θ) = sin(π+θ)
=> 4θ = 2nπ ± θ and 4θ = nπ + (-1)n(π+θ)
=> 4θ = 2nπ-θ
=> θ=2nπ/5
341you missed z=0. Which is why you must write out why you assumed z=e1θ.
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