It seems that even if you don't have a good idea how to arrive at an answer, you have an obvious starting path: plug the answer form "z=a+bi" into the equation you're trying to solve. It may, or it may not, lead to something that works, but at least it's something to try.static said:Determine all solutions of z^2 = 1+2i in the form z=a+bi, where a and b are real numbers.
For this question numerical evaluation is not required. I just don't know how to start.
Complex numbers are numbers that contain both a real and imaginary component. They are written in the form a + bi, where a is the real part and bi is the imaginary part, with i representing the square root of -1.
Complex numbers are used to represent quantities that cannot be expressed using only real numbers. They are commonly used in mathematical equations and in various fields such as engineering, physics, and economics.
To add or subtract complex numbers, you simply add or subtract the real and imaginary parts separately. For example, (2 + 3i) + (4 + 5i) = 6 + 8i and (2 + 3i) - (4 + 5i) = -2 - 2i.
Multiplying complex numbers is similar to multiplying polynomials. You multiply the real parts and the imaginary parts separately, then combine them. For example, (2 + 3i)(4 + 5i) = 8 + 12i + 10i + 15i^2 = -7 + 22i. To divide complex numbers, you must first multiply the numerator and denominator by the complex conjugate of the denominator, then simplify.
Complex numbers have many applications in the real world, such as in electrical engineering for analyzing AC circuits, in signal processing for analyzing sound and images, and in economics for modeling financial data. They are also used in computer graphics for creating 3D images and animations.