MCS 351 ENGINEERING MATHEMATICS SOLUTION OF ...
MCS 351 ENGINEERING MATHEMATICS SOLUTION OF ...
MCS 351 ENGINEERING MATHEMATICS SOLUTION OF ...
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• t = π ⇒ z(π) = 3 + 4i + 5e iπ = 3 + 4i + 5(cos π + i sin π) = −2 + 4i<br />
• t = 2π ⇒ z(2π) = 3 + 4i + 5e i2π = 3 + 4i + 5(cos 2π + i sin 2π) = 8 + 4i<br />
7. z(t) = 6 cos 2t + i5 sin 2t, 0 ≤ t ≤ π. Let x(t) = 6 cos 2t and y(t) = 5 sin 2t.<br />
• t = 0 ⇒ z(0) = 6<br />
• t = π 2<br />
⇒ z( π 2 ) = −6<br />
• t = π ⇒ z(π) = 6<br />
This parametric equation denotes the ellipse below:<br />
8. z(t) = 1 + 2t + 8it 2 , −1 ≤ t ≤ 1 denotes parabola.<br />
• t = −1 ⇒ z(−1) = −1 + 8i<br />
• t = 0 ⇒ z(0) = 1<br />
• t = 1 ⇒ z(1) = 3 + 8i<br />
9. z(t) = 1 + 1 2 it3 , −1 ≤ t ≤ 2<br />
• t = −1 ⇒ z(−1) = −1 − 1 2 i 27