# rev6 - z 1 | | z 2 | and d | z 1-z 2 | ≥ ³ ³ | z 1 | |...

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Physics (PHZ) 3113 Florida Atlantic University Mathematical Physics Fall, 2009 Review Problems VI Recommended Reading: Chow, pp. 233–238. 1. (Chow 6.2) Given the complex numbers z 1 := 3 + 4i 3 - 4i and z 2 := ± 1 + 2i 1 - 3i ² 2 , ﬁnd their polar forms, complex conjugates, moduli, product, and quotients. 2. (Chow 6.3) The absolute value or modulus of a complex number z =: x + i y is deﬁned as | z | = zz * = p x 2 + y 2 . If z 1 and z 2 are complex numbers, show that: a. | z 1 z 2 | = | z 1 || z 2 | , b. | z 1 /z 2 | = | z 1 | / | z 2 | for z 2 6 = 0, c. | z 1 + z 2 | ≤ |
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Unformatted text preview: z 1 | + | z 2 | , and d. | z 1-z 2 | ≥ ³ ³ | z 1 | - | z 2 | ³ ³ . 3. (Chow 6.4) Find all possible complex values of z (a) := 5 √-32 and z (b) := 3 √ 1 + i , and plot them in the complex plane. 4. (Chow 6.5) Use De Moivre’s theorem to show that a. cos 5 θ = 16 cos 5 θ-20 cos 3 θ + 5 cos θ , and b. sin 5 θ = 5 cos 4 θ sin θ-10 cos 2 θ sin 3 θ + sin 5 θ ....
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