Question

Find the value of $e^{6^{deg}i}$ $\times$ $e^{9^{deg}i}$ $\times$ $e^{{13}^{deg}i}$ $\times$ $e^{{17}^{deg}i}$ (where deg = degree)

• A. i
• B. $\frac{1+i}{\sqrt{2}}$
• C. $\frac{1-i}{\sqrt{2}}$
• D. $\frac{i}{\sqrt{2}}$

Answer 1

The correct option is B $\frac{1+i}{\sqrt{2}}$

$e^{6^{deg}i}$ $\times$ $e^{9^{deg}i}$ $\times$ $e^{{13}^{deg}i}$ $\times$ $e^{{17}^{deg}i}$

= $e^{(6^{deg}+9^{deg}i+{13}^{deg}i+{17}^{deg}i)}$

=$e^{{45}^{deg}i}$

${45}^{deg}$ can also be written as $\frac{\pi }{4}$

= $e^{i\frac{\pi }{4}}$

=cos $\frac{\pi }{4}$ + i sin $\frac{\pi }{4}$

= $\left(\frac{1+i}{\sqrt{2}}\right)$