 # Express the following in the form T 20, where the angle is in the p...

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Express the following in the form T 20, where the angle is in the principal form and in the form a + ib. (a) 6 W= 3+ i (b) 10 w = 1 - Let z = x+iy. Describe in words the portion of the complex plane corresponding to the equation ziz = Imz. Or state whether problem has no solutions, i.e., is satisfied only by the null set. Find all three roots of Z = Express the complex number ee' in the form a + ib. Find all values of the logarithm of ee and state the principal value. Put answer in the form a + ib. Give the solutions to the equation (Logz² + 2Logz = - -2. Let z = x + iy and consider the function = - - (i) at what points does the derivative exist? (ii) derive a formula for the derivative of f(z), where the derivative exists. (iii) Hence evaluate the derivative of f(z) at 2 = i. (iv) where is function f analytic? State the region of analyticity of the function f(z) = Log(z + 2+3i).

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