Algebra

De Moivre's Theorem

De Moivre's Theorem - Raising to a Power

         

Evaluate (2+i22)64.\left(\frac{\sqrt{2}+i\sqrt{2}}{2}\right)^{64}.

Let zz be a complex number such that z=2(cos4+isin4).z = \sqrt{2}(\cos 4 ^{\circ} + i \sin 4 ^{\circ}). Then z8 z^{8} can be expressed as r(cosα+isinα) r( \cos \alpha^{\circ} + i \sin \alpha^{\circ}) , where rr is a real number and 0α90 0 \leq \alpha \leq 90. What is the value of r+α?r+\alpha ?

Details and assumptions

ii is the imaginary number such that i2=1i^2=-1.

What is the value of (cosπ8+isinπ8)16\left( \cos \frac{\pi}{8} + i \sin \frac{\pi}{8} \right)^{16} ?

Details and assumptions

ii is the imaginary unit, where i2=1i^2=-1.

If x=cosπ14+isinπ14,y=cos914π+isin914π,\begin{aligned} x & =\cos \frac{\pi}{14}+i\sin \frac{\pi}{14},\\ y &= \cos \frac{9}{14}\pi+i\sin \frac{9}{14}\pi, \end{aligned} what is the value of x5y15x^{5} y^{15}?

×

Problem Loading...

Note Loading...

Set Loading...