Express the following in the form T 20, where the angle is in the principal form and
in the form a + ib.
W= 3+ i
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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