End-of-chapter review exercise 23: 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.
End-of-chapter review exercise 23: 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.
End-of-chapter review exercise 23: 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.
End-of-chapter review exercise 23: 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.
End-of-chapter review exercise 23: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Find the roots of \(\displaystyle z^{3}= 14^{3}e^{\frac{i\pi }{2}}\). For angle answers use radians and arguments in [0,2π).
Find the angular spacing between successive roots.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
End-of-chapter review exercise 23: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Find the roots of \(\displaystyle z^{4}= 15^{4}e^{\frac{i\pi }{3}}\). For angle answers use radians and arguments in [0,2π).
Find the angular spacing between successive roots.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
End-of-chapter review exercise 23: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 3e^{\frac{i\pi }{6}}\) and \(S=\sum_{k=0}^{3}z^k\).
Find the real part of the sum from \(\displaystyle k=1\) to \(\displaystyle k=4\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
End-of-chapter review exercise 23: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 4e^{\frac{i\pi }{7}}\) and \(S=\sum_{k=0}^{4}z^k\).
Find the real part of the sum from \(\displaystyle k=1\) to \(\displaystyle k=5\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.