de Moivre's theorem: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 4[\cos (\frac{\pi }{5})+ i\sin (\frac{\pi }{5})]\), with \(\displaystyle n=4\).
Find the modulus of \(\displaystyle z^{n}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
de Moivre's theorem: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 5[\cos (\frac{\pi }{6})+ i\sin (\frac{\pi }{6})]\), with \(\displaystyle n=5\).
Find the modulus of \(\displaystyle z^{n}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
de Moivre's theorem: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 5[\cos (\frac{\pi }{6})+ i\sin (\frac{\pi }{6})]\), with \(\displaystyle n=5\).
Find \(\displaystyle \operatorname{Re}(z^{n})\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
de Moivre's theorem: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 2[\cos (\frac{\pi }{3})+ i\sin (\frac{\pi }{3})]\), with \(\displaystyle n=3\).
Find \(\displaystyle \operatorname{Re}(z^{n})\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
de Moivre's theorem: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 2[\cos (\frac{\pi }{3})+ i\sin (\frac{\pi }{3})]\), with \(\displaystyle n=3\).
Find \(\displaystyle \operatorname{Im}(z^{n})\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
de Moivre's theorem: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 5[\cos (\frac{\pi }{6})+ i\sin (\frac{\pi }{6})]\), with \(\displaystyle n=3\).
Find \(\displaystyle \operatorname{Im}(z^{n})\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
de Moivre's theorem: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 3[\cos (\frac{\pi }{4})+ i\sin (\frac{\pi }{4})]\), with \(\displaystyle n=4\).
Find \(\displaystyle |z^{n}|^{2}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
de Moivre's theorem: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 4[\cos (\frac{\pi }{5})+ i\sin (\frac{\pi }{5})]\), with \(\displaystyle n=5\).
Find \(\displaystyle |z^{n}|^{2}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.