hw4 - MAT22B–1 HW 4...

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Unformatted text preview: MAT22B–1: HW 4 ————————————————————————————————————————— Definition 1 (Euler’s Formula) eiθ = cos θ + i sin θ. Some Trigonometric Identities: cos(θ + φ) = cos θ cos φ − sin θ sin φ cos(θ − φ) = cos θ cos φ + sin θ sin φ sin(θ + φ) = cos θ sin φ + cos φ sin θ sin(θ − φ) = cos θ sin φ − cos φ sin θ. ————————————————————————————————————————— Do the following problems 1. Use Euler’s Formula to write the given expression in the form a + ib. i. eiπ ii. e2−3i 2. Use Euler’s Formula to show that i. cos θ = eiθ +e−iθ 2 ii. sin θ = eiθ −e−iθ 2i 3. Show that eit dt = 1 eit in two different ways i i. by using the Euler’s Formula ii. by using the fact that d it [e ] dt = ieit . 1 ...
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