A complex logarithm is a mathematical function that calculates the logarithm of a complex number. It is defined as the inverse of the exponential function, and can be written as logb(z) = x + iy, where z is the complex number, b is the base of the logarithm, and x and y are real numbers.
To solve for a complex logarithm, you can use the formula logb(z) = x + iy. First, convert the complex number into polar form (r(cosθ + isinθ)). Then, apply the formula logb(z) = logb(r) + iθ. Finally, use the properties of logarithms to simplify the equation and find the values of x and y.
Tan-1 (also written as arctan) is the inverse trigonometric function for tangent. In this expression, it is used to find the angle whose tangent is equal to the complex number (2sqrt(3) - 3i)/7.
To solve for the complex logarithm of a complex number, you can follow the same steps as solving for a real logarithm. First, convert the complex number into polar form. Then, apply the formula logb(z) = logb(r) + iθ. Finally, simplify the equation using properties of logarithms and solve for the values of x and y.
Solving for tan-1[(2sqrt(3) - 3i)/7] in the complex logarithm allows you to find the angle whose tangent is equal to the complex number (2sqrt(3) - 3i)/7. This is useful in many applications, such as in engineering, physics, and signal processing.