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

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

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

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

Express $6\bigl(\cos\tfrac{5\pi}{4}+i\sin\tfrac{5\pi}{4}\bigr)$ in Cartesian form.

Convert $10\bigl(\cos\tfrac{3\pi}{2}+i\sin\tfrac{3\pi}{2}\bigr)$ into $a+bi$ form.

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

Express $12\bigl(\cos\tfrac{11\pi}{6}+i\sin\tfrac{11\pi}{6}\bigr)$ in Cartesian form.

Convert $5\bigl(\cos(-\tfrac{\pi}{3})+i\sin(-\tfrac{\pi}{3})\bigr)$ to Cartesian form.

Express $2\sqrt3\bigl(\cos\tfrac{\pi}{6}+i\sin\tfrac{\pi}{6}\bigr)$ in Cartesian form.

Express $7\bigl(\cos\tfrac{4\pi}{3}+i\sin\tfrac{4\pi}{3}\bigr)$ in Cartesian form.

Convert $3.5\bigl(\cos\tfrac{5\pi}{4}+i\sin\tfrac{5\pi}{4}\bigr)$ into $a+bi$ form.

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