6 4 x y 2 1 y 1 1 x 2et t 0 2 t 1 1 y e2t

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Unformatted text preview: ) is a set, we will write ‘θ ∈ arg(z )’ to mean ‘θ is in the set of arguments of z .’ The symbol being used here, ‘∈,’ is the mathematical symbol which denotes membership in a set. 4 If we had Calculus, we would regard Arg(0) as an ‘indeterminate form.’ But we don’t, so we won’t. 5 In this solution, we take the time to review how to convert from rectangular coordinates into polar coordinates in great detail. In future examples, we do not. Review Example 11.4.2 in Section 11.4 as needed. 6 See Example 10.6.7 in Section 10.6 for review, if needed. 3 844 Applications of Trigonometry 3. We rewrite z = 3i as z = 0 + 3i to find Re(z ) = 0 and Im(z ) = 3. The point in the plane which corresponds to z is (0, 3) and while we could go through the usual calculations to find the required polar form of this point, we can almost ‘see’ the answer. The point (0, 3) lies 3 units away from the origin on the positive y -axis. Hence, r = |z | = 3 and θ = π + 2πk for 2 integers k . We get arg(z ) = π + 2πk : k is an in...
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