Simplify Complex Operations

Investigate how to operate on complex numbers.

As compared to real numbers, a new dimension represented by the imaginary number jj is added in the complex representation. A complex number VV is simply a combination of two real numbers, one on the real axis and one on the imaginary axis, as shown in the figure below. We call the x-component VIV_I and the y-component VQV_Q.

VI=AcosθVQ=Asinθ\begin{equation}\begin{aligned} V_I &= A\cos \theta \\ V_Q &= A\sin \theta \end{aligned} \end{equation}

where AA is the distance from the origin (magnitude) and θ\theta is the angle from the x-axis.

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