Complex Current Divider

An AC current source feeds a circuit with the complex impedances shown in the diagram. The circuit acts as a current divider, with part of the injected current flowing through the left branch and part of it flowing through the right branch.

If the currents in the left and right branches are perfectly in-phase with each other, determine the value of \(x\) (to 2 decimal places).

Clarification: \(x\) is a positive real number. The symbol \(j\) denotes the imaginary unit.

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