Express each of the following complex numbers in Cartesian form, i.e., $x+iy$, where $x$ an

Question

Express each of the following complex numbers in Cartesian form, i.e., $x+iy$, where $x$ and $y$ are real numbers. $3\left( \cos \frac{\pi}{6} + i \sin \frac{\pi}{6} \right)$ $7\left( -\cos \frac{\pi}{4} + i \sin \frac{\pi}{4} \right)$ $2\left( \cos \frac{\pi}{3} + i \sin \frac{\pi}{4} \right)$

Accepted Answer

(i) $\frac{3\sqrt3}{2}+\frac32i$; (ii) $-\frac{7\sqrt2}{2}+\frac{7\sqrt2}{2}i$; (iii) $1+\sqrt2\,i$.

Conversion of forms

Conversion of forms

Solution:

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