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5. ( Euler's identity and complex numbers. (a) Use Euler's formula to prove the following identities: i. cos (0) + sin?(0) = 1 2 ii. cos(0 + ) = cos(0) cos() – sin(@) sin()| %3D (Ъ) r(t) = (5+ v2j)e³(t+2) and y(t) = 1/(2 – j). i. Compute the real and imaginary parts of r(t) and y(t). ii. Compute the magnitude and phase of r(t) and y(t).

5. ( Euler's identity and complex numbers. (a) Use Euler's formula to prove the following identities: i. cos (0) + sin?(0) = 1 2 ii. cos(0 + ) = cos(0) cos() – sin(@) sin()| %3D (Ъ) r(t) = (5+ v2j)e³(t+2) and y(t) = 1/(2 – j). i. Compute the real and imaginary parts of r(t) and y(t). ii. Compute the magnitude and phase of r(t) and y(t).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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5. ( Euler's identity and complex numbers. (a) Use Euler's formula to prove the following identities: i. cos (0) + sin?(0) = 1 ii. cos(0 + v) = cos(4) cos() – sin(0) sin()| (b) x(t) = (5+ v2j)e(++2) and y(t) = 1/(2- j). i. Compute the real and imaginary parts of r(t) and y(t). ii. Compute the magnitude and phase of r(t) and y(t).
Transcribed Image Text:5. ( Euler's identity and complex numbers. (a) Use Euler's formula to prove the following identities: i. cos (0) + sin?(0) = 1 ii. cos(0 + v) = cos(4) cos() – sin(0) sin()| (b) x(t) = (5+ v2j)e(++2) and y(t) = 1/(2- j). i. Compute the real and imaginary parts of r(t) and y(t). ii. Compute the magnitude and phase of r(t) and y(t).
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