Αποτελέσματα Αναζήτησης
8(1 z2)3z; (c) 1=(2z + 1)2; (d) e1=z=z2. 8. Prove the following version of complex L’Hospital: Let f (z) and g(z) be two complex functions defined on jz z0j < r for some r > 0. Suppose that f (z0) = g(z0) = 0, f (z) and g(z) are differentiable at z0 and g0(z0) 6= 0. Then.
The problems covered include finding the general value of log(1+i)+log(1-i), evaluating logarithms of expressions involving trigonometric functions, and using properties of logarithms to simplify complex logarithmic expressions.
This document contains several unsolved problems involving logarithms of complex numbers. The problems involve proving various identities related to taking logarithms and separating results into real and imaginary parts for expressions involving complex numbers and trigonometric functions.
Examples for Complex numbers Question (01) (i) Find the real values of x and y such that (1 ) 2 (2 3 ) 3 3 i x i i y i i i i − + + + + =− − + (ii) Find the real values of x and y are the complex numbers 3−ix y2 and − − −x y i2 4 conjugate of each other. (iii) Find the square roots of 4 4+i (iv) Find the complex number Z satisfying ...
Complex numbers - Exercises with detailed solutions 1. Compute real and imaginary part of z = i¡4 2i¡3: 2. Compute the absolute value and the conjugate of z = (1+ i)6; w = i17: 3. Write in the \algebraic" form (a+ib) the following complex numbers z = i5 +i+1; w = (3+3i)8: 4. Write in the \trigonometric" form (‰(cosµ +isinµ)) the following ...
In these notes, we examine the logarithm, exponential and power functions, where the arguments∗ of these functions can be complex numbers. In particular, we are interested in how their properties differ from the properties of the corresponding real-valued functions.†. 1. Review of the properties of the argument of a complex number.
Because equation 3.21 yields logarithms of every nonzero complex number, we have defined the complex logarithm function. It is defined for all z 6= 0, and because arg z is determined only to a multiple of 2π, each nonzero complex number has an infinite number of logarithms. For example, √.
