The roots of unity: check 1
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 common modulus of the roots.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The roots of unity: review variant 1
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 common modulus of the roots.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The roots of unity: check 2
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 smallest nonnegative root argument.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The roots of unity: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
Find the roots of \(\displaystyle z^{5}= 16^{5}e^{\frac{i\pi }{4}}\). For angle answers use radians and arguments in [0,2π).
Find the smallest nonnegative root argument.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The roots of unity: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Find the roots of \(\displaystyle z^{5}= 16^{5}e^{\frac{i\pi }{4}}\). 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.
The roots of unity: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
Find the roots of \(\displaystyle z^{6}= 17^{6}e^{\frac{i\pi }{2}}\). 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.
The roots of unity: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Find the roots of \(\displaystyle z^{6}= 17^{6}e^{\frac{i\pi }{2}}\). For angle answers use radians and arguments in [0,2π).
Find the real part of the root with smallest nonnegative argument.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
The roots of unity: review variant 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
Find the roots of \(\displaystyle z^{3}= 18^{3}e^{\frac{i\pi }{3}}\). For angle answers use radians and arguments in [0,2π).
Find the real part of the root with smallest nonnegative argument.
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.