Question

Write the following complex number in rectangular form. 6(cos π/ 4+ isin π/ 4)

6(cos π/ 4 + i sin π/ 4) =
​(Simplify your answer. Type an exact​ answer, using radicals as needed. Use integers or fractions for any numbers in the expression. Type your answer in the form a+bi. Rationalize all​ denominators.)

Answer 1

`\stackrel{\textit{complex form}}{\stackrel{\stackrel{r}{\downarrow }}{6}\left[ \cos\left( (\pi )/(4) \right) +i\sin\stackrel{\stackrel{\theta }{\downarrow }}{\left( (\pi )/(4) \right)} \right]}\implies 6\left[ (√(2))/(2)+i(√(2))/(2) \right]\implies \cfrac{6√(2)}{2}+i\cfrac{6√(2)}{2} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{rectangular form}}{\stackrel{\stackrel{a}{\downarrow }}{3√(2)}+\stackrel{\stackrel{b}{\downarrow }}{3√(2)}i}~\hfill`