6. Evaluate the following complex integrals. (a) ?_C ?dz, where C is the circle |z - 1| = 1, traversed counterclockwise. (b) ?_C z^2dz, where C is the line segment traversed from 1 to 2 + i. (c) ?_C sin(z^2019)dz, where C is the circle |z| = 2019, traversed clockwise.

          6. Evaluate the following complex integrals.

(a) ?_C ?dz, where C is the circle |z - 1| = 1, traversed counterclockwise.

(b) ?_C z^2dz, where C is the line segment traversed from 1 to 2 + i.

(c) ?_C sin(z^2019)dz, where C is the circle |z| = 2019, traversed clockwise.

6. Evaluate the following complex integrals.

(a) ?C ?dz, where C is the circle |z - 1| = 1, traversed counterclockwise.

(b) ?C z^2dz, where C is the line segment traversed from 1 to 2 + i.

(c) ?C sin(z^2019)dz, where C is the circle |z| = 2019, traversed clockwise.

Added by Silvia E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

05/31/2023

Step 1

We can parametrize the circle as $z(\theta) = \frac{1}{2} + \frac{1}{2}e^{i\theta}$, where $0 \leq \theta \leq 2\pi$. Then, $dz = \frac{1}{2}ie^{i\theta} d\theta$. Substituting this into the integral, we get $$\oint_C z \, dz = \int_0^{2\pi} \left(\frac{1}{2} + Show more…

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6. Evaluate the following complex integrals. (a) ∫_C Źdz, where C is the circle |z - 1| = 1, traversed counterclockwise. (b) ∫_C z^2dz, where C is the line segment traversed from 1 to 2 + i. (c) ∫_C sin(z^2019)dz, where C is the circle |z| = 2019, traversed clockwise.