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Home » \[ 4 \cdot i = 4i \] - AMAZONAWS

\[ 4 \cdot i = 4i \] - AMAZONAWS

📅 March 6, 2026 👤 scraface

Mar 06, 2026

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📌 \cos(z) = 0 \quad \Rightarrow \quad z = 90^\circ, \quad z = 270^\circ

📌 We verify these solutions in the original equation:

📌 For \(z = 90^\circ\), \(\sin(180^\circ) = 0\) and \(\cos(90^\circ) = 0\), so it satisfies.

📌 For \(z = 270^\circ\), \(\sin(540^\circ) = 0\) and \(\cos(270^\circ) = 0\), so it satisfies.

📌 Thus, the angles \(z \in [0^\circ, 360^\circ]\) that satisfy the equation are:

📌 z = 30^\circ, \quad 150^\circ, \quad 90^\circ, \quad 270^\circ

📌 oxed{30^\circ, 90^\circ, 150^\circ, 270^\circ}

📌 An electrical engineer is optimizing a power grid model and encounters a transformation matrix problem. Find the \(2 imes 2\) matrix \(\mathbf{M}\) such that for any vector \(\mathbf{v} = egin{bmatrix} x \ y \end{bmatrix}\), the transformation satisfies \(\mathbf{M}\mathbf{v} = egin{bmatrix} x + 2y \ 3x - y \end{bmatrix}\).

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