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==Complex numbers and Complex Analysis==
If you apply a voltage across a capacitor, it 'charges up' by storing the electrical charge as an electrical field inside the device. This means that while the voltage across the capacitor remains initially small, a large current flows. Later, the current flow is smaller because the capacity is filled, and the voltage raises across the device. Complex Analysis methods are also important in electrical engineering in fields such as signal processing, power electronics, control systems, and others.
A similar though opposite situation occurs in an inductor; the applied voltage remains high with low current as a magnetic field is generated, and later becomes small with high current when the magnetic field is at maximum.
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