The polar form $R \angle \theta$ signifies a phasor with magnitude $R$ and phase angle $\theta$.

In the rectangular form $x + jy$, $x$ represents the real (in-phase) component and $y$ represents the imaginary (quadrature) component.

The value of $\cos(30°) = \frac{\sqrt{3}}{2}$ and $\sin(30°) = 0.5$.

Polar form is highly efficient for multiplication and division of complex numbers.

Rectangular form is ideal for addition and subtraction of complex numbers.

Conversion between forms can lead to rounding errors if not performed with exact trigonometric values.

AC circuit analysis (phasor diagrams)

Control system frequency response analysis

Signal processing

Option B represents $10\sqrt{3} + j2$, which does not correspond to the magnitude of 10.

Option C represents $\sqrt{3} + j5$, which is mathematically incorrect for this magnitude.

Option D represents $15\sqrt{3} + j3$, which is significantly larger than the input magnitude.