If \(\gamma(t)=e^{it}\), what is \(\gamma'(t)\)?

Study Complex analysis in ZWMath →

Review the concept: Curve and contour

A smooth curve \(\gamma\) is a function from a real interval \([a,b]\) into \(\mathbb{C}\) with continuous, nonzero derivative; a contour is a finite chain of smooth curves joined end to end.

More practice problems: curve and contour

• ZW-CURVE-AND-CONTOUR-001 For the curve γ(t)=t+it^2, 0≤ t≤1, find the endpoint γ(1).
• ZW-CURVE-AND-CONTOUR-003 What curve does γ(t)=2+3e^it, 0≤ t≤2π, describe?
• ZW-CURVE-AND-CONTOUR-004 Which one parametrizes the segment from 1 to i with 0≤ t≤1?
• ZW-CURVE-AND-CONTOUR-005 Compute the length of γ(t)=3t+4it, 0≤ t≤2, using L=∫_a^b|γ'(t)| dt.
• ZW-CURVE-AND-CONTOUR-006 For γ(t)=t+it^2, compute |γ'(1)|.
• ZW-CURVE-AND-CONTOUR-007 How many smooth curves make up the contour tracing the boundary of a triangle?
• ZW-CURVE-AND-CONTOUR-008 Is γ(t)=t^3+it^3 a smooth curve on [-1,1]? Its image is a segment.
• ZW-CURVE-AND-CONTOUR-009 Let γ(t)=e^it, 0≤ t≤π, going from 1 to -1. Which one parametrizes the opposite curve -γ with 0≤ t≤π?

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