Project ID:
7200000055
Accepted:
Type:
Layout:
Question:
Match each power of a complex number with its corresponding result of exponentiation in algebraic form.
Questions Title:
Power of a Complex Number
Answers Title:
Result of Exponentiation
Question 1:
$$\left(\cos\frac{5}{3}\pi+\mathrm{i}\cdot\sin\frac{5}{3}\pi\right)^{12}$$
Answer 1:
$$1$$
Question 2:
$$\left(\cos\frac{7}{6}\pi+\mathrm{i}\cdot\sin\frac{7}{6}\pi\right)^{28}$$
Answer 2:
$$-\frac{1}{2}+\mathrm{i}\cdot\frac{\sqrt3}{2}$$
Question 3:
$$\left(\frac{\sqrt2}{2}-\mathrm{i}\cdot\frac{\sqrt2}{2}\right)^{15}$$
Answer 3:
$$\frac{\sqrt2}{2}+\mathrm{i}\cdot\frac{\sqrt2}{2}$$
Question 4:
$$\left(\cos\frac{3}{4}\pi+\mathrm{i}\cdot\sin\frac{3}{4}\pi\right)^{-7}$$
Answer 4:
$$-\frac{\sqrt2}{2}+\mathrm{i}\cdot\frac{\sqrt2}{2}$$
Question 5:
$$\left(\cos\frac{5}{6}\pi+\mathrm{i}\cdot\sin\frac{5}{6}\pi\right)^{-45}$$
Answer 5:
$$\mathrm{i}$$
Question 6:
$$\left(\cos\frac{\pi}{4}+\mathrm{i}\cdot\sin\frac{\pi}{4}\right)^{22}$$
Answer 6:
$$-\mathrm{i}$$
Answer 7:
$$\frac{\sqrt3}{2}-\mathrm{i}\cdot\frac{1}{2}$$
Answer 8:
$$-\frac{\sqrt3}{2}+\mathrm{i}\cdot\frac{1}{2}$$