(c) Express $$ Z=5\left(\cos 60^{\circ}+i \sin 60^{\circ}\right) $$ in Euler's form

Question

UpStudy AI · Accepted Answer

Given 
$$
Z=5\left(\cos 60^{\circ}+i \sin 60^{\circ}\right),
$$
we recognize that Euler's formula states
$$
e^{i\theta} = \cos \theta + i \sin \theta.
$$

1. Identify $$\theta$$. Here, $$\theta = 60^{\circ}$$.
2. Convert $$60^{\circ}$$ into radians:
   $$
   60^{\circ}=\frac{\pi}{3}.
   $$
3. Substitute $$\theta = \frac{\pi}{3}$$ into Euler's formula:
   $$
   \cos 60^{\circ}+i \sin 60^{\circ} = e^{i\pi/3}.
   $$
4. Therefore, the expression for $$Z$$ in Euler's form is:
   $$
   Z=5e^{i\pi/3}.
   $$
$$ Z = 5e^{i\pi/3} $$

© Express in Euler’s form

Upstudy AI Solution

Answer

Solution

The Deep Dive

Related Questions

Latest Pre Calculus Questions