Project ID:
7200000042
Accepted:
Type:
Layout:
Question:
Let $a$, $b$, and $c$ be complex numbers, where:
$$\begin{aligned}
a &= 4\left(\cos \frac{7\pi}{6} + \mathrm{i} \sin \frac{7\pi}{6}\right),\cr
b &= \cos \frac{5\pi}{6} + \mathrm{i} \sin \frac{5\pi}{6},\cr
c &= 2\left(\cos \frac{2\pi}{3} + \mathrm{i} \sin \frac{2\pi}{3}\right).\
\end{aligned}$$
Match the given complex expressions with their corresponding values expressed in polar form.
Questions Title:
Expression with complex numbers
Answers Title:
Value in polar form
Question 1:
$$\frac{a}{b}$$
Answer 1:
$$4\left(\cos \frac{\pi}{3} + \mathrm{i} \sin \frac{\pi}{3}\right)$$
Question 2:
$$c^2$$
Answer 2:
$$4\left(\cos \frac{4\pi}{3} + \mathrm{i} \sin \frac{4\pi}{3}\right)$$
Question 3:
$$b\cdot c$$
Answer 3:
$$2\left(\cos \frac{3\pi}{2} + \mathrm{i} \sin \frac{3\pi}{2}\right)$$
Question 4:
$$\frac{a\cdot c}{b}$$
Answer 4:
$$8\left(\cos \pi + \mathrm{i} \sin \pi\right)$$
Question 5:
$$\left(\frac{a\cdot b}{c}\right)^2$$
Answer 5:
$$4\left(\cos \frac{2\pi}{3} + \mathrm{i} \sin \frac{2\pi}{3}\right)$$
Question 6:
$$\frac{a^3\cdot b}{c^4}$$
Answer 6:
$$4\left(\cos \frac{5\pi}{3} + \mathrm{i} \sin \frac{5\pi}{3}\right)$$
Answer 7:
$$2\left(\cos \frac{4\pi}{3} + \mathrm{i} \sin \frac{4\pi}{3}\right)$$
Answer 8:
$$8\left(\cos \frac{2\pi}{3} + \mathrm{i} \sin \frac{2\pi}{3}\right)$$