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# B now do several checks first make sure the units

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Unformatted text preview: nitude. (b) Now do several checks. First, make sure the units worked out (!) The, ﬁnd the magnitude of the force in the limit L → 0. What do you expect? Brieﬂy, discuss. Lastly, ﬁnd the magnitude of the force in the limit d → ∞ ? Again, is it what you expect? Brieﬂy, discuss. Figure 2: 3. Practicing with complex numbers. (1 pt each) √ (a) If z1 = − 3 + i, draw z1 in the complex plane. Compute its real and imaginary parts and magnitude. Write z1 as Aeiθ and determine A and θ. (b) If z2 = 1/(1 + i), draw z in the complex plane. Compute its real and imaginary parts and magnitude. Write z as Aeiθ and determine A and θ. 2 (c) What are the real and imaginary parts of 1/z3 with z3 = 0.5e−iπ/3 . (d) Compute Z = z1 ∗ z3 with z1 and z3 given in parts (a) and (c). Draw Z in the complex plane. Compute its real and imaginary parts and magnitude. Write Z as Aeiθ and determine A and θ. CONTINUED –2– PHYS 2210 4. Consider again the simple pendulum problem. In homework 7 you showed that the pendulum’s potential energy (measured from the equilibrium level ) is U (φ) = mgL(1 − cos φ) (where L is ￿ pendulum length) the and that under the sm...
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