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8 results for “complex”

Formulae (8)

e^{i\theta} = \cos\theta + i\sin\theta

Links complex exponentials to trigonometry.

(\cos\theta + i\sin\theta)^n = \cos n\theta + i\sin n\theta

Powers of complex numbers in trig form.

T(n) = aT(n/b) + f(n)

Analyzes running time of divide-and-conquer algorithms.

O(1) < O(\log n) < O(n) < O(n\log n) < O(n^2) < O(2^n)

Ordering of common algorithmic growth rates.

O(\log n)

Runtime that grows logarithmically with input size.

O(n\log n)

Runtime of efficient comparison sorts.

O(n^2)

Runtime that grows with the square of input size.

O(2^n)

Runtime that doubles with each added element.