Complex summations: check 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 2e^{\frac{i\pi }{7}}\) and \(S=\sum_{k=0}^{3}z^k\).
Find Re(S).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Complex summations: review variant 1
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 3e^{\frac{i\pi }{3}}\) and \(S=\sum_{k=0}^{4}z^k\).
Find Re(S).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Complex summations: check 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 3e^{\frac{i\pi }{3}}\) and \(S=\sum_{k=0}^{4}z^k\).
Find Im(S).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Complex summations: review variant 2
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 4e^{\frac{i\pi }{4}}\) and \(S=\sum_{k=0}^{5}z^k\).
Find Im(S).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Complex summations: check 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 4e^{\frac{i\pi }{4}}\) and \(S=\sum_{k=0}^{5}z^k\).
Find \(\displaystyle |S|^{2}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Complex summations: review variant 3
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 2e^{\frac{i\pi }{5}}\) and \(S=\sum_{k=0}^{2}z^k\).
Find \(\displaystyle |S|^{2}\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Complex summations: check 4
Difficulty: ★★☆Info
Maths4U Original · Short practice
\(\displaystyle z= 2e^{\frac{i\pi }{5}}\) and \(S=\sum_{k=0}^{2}z^k\).
Find the real part of the sum from \(\displaystyle k=1\) to \(\displaystyle k=3\).
Enter one number or fraction. Use at least six decimal places when needed; a distribution calculator may be used for probabilities.
Complex summations: review variant 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.