Question Type 3: Converting complex numbers from Polar to Cartesian form Exercises

Express $6\left(\cos\frac{5\pi}{4}+i\sin\frac{5\pi}{4}\right)$ in Cartesian form.

Express $5\bigl(\cos\tfrac{5\pi}{12}+i\sin\tfrac{5\pi}{12}\bigr)$ in Cartesian form, using exact surds.

Express $12\left(\cos \frac{11\pi}{6} + i \sin \frac{11\pi}{6}\right)$ in Cartesian form.

Convert $3.5\left(\cos\frac{5\pi}{4}+i\sin\frac{5\pi}{4}\right)$ into $a+bi$ form.

Express $3\bigl(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6}\bigr)$ in the form $a+bi$.

Express $7\left(\cos\frac{4\pi}{3} + i\sin\frac{4\pi}{3}\right)$ in Cartesian form.

Convert $10\left(\cos\frac{3\pi}{2}+i\sin\frac{3\pi}{2}\right)$ into $a+bi$ form.

Express $4\bigl(\cos\frac{\pi}{4}+i\sin\frac{\pi}{4}\bigr)$ in Cartesian form.

Convert $5\left(\cos\left(-\frac{\pi}{3}\right)+i\sin\left(-\frac{\pi}{3}\right)\right)$ to Cartesian form.

Convert $8\left(\cos\frac{2\pi}{3} + i\sin\frac{2\pi}{3}\right)$ to Cartesian form.

Convert $5\bigl(\cos\frac{\pi}{3}+i\sin\frac{\pi}{3}\bigr)$ into Cartesian form.

Express $2\sqrt3\left(\cos\frac{\pi}{6}+i\sin\frac{\pi}{6}\right)$ in Cartesian form.