One of the main complaints that students have when struggling with their math homework is that they don't understand why they need to learn this in the first place. After all, how often do we actually use calculus or trigonometry in our daily lives? I always make an effort to correct this false assumption in my students. Everything that we learn in math connects to reality... read more
Laplace equations also included for z=x+iy domain, polar Cauchy/Riemann form included
Using techniques from complex analysis, sin z can be factored just as any polynomial.
Hint 1; Complex numbers are not more complicated than any other numbers, just different. Complex number = real number + imaginary number Hint 2; imaginary numbers are not more ethereal than real numbers, just different. Imaginary numbers were invented to solve problems involving square roots of negative numbers. Hint 3; we lied to you when we told you that you cannot take the... read more
Complex Numbers Written by tutor Colin D. How to Envision Complex Numbers Graphically: The Complex Plane The complex number x + yi corresponds to the point with coordinates (x, y) The x-axis is the real axis The y-axis is the imaginary axis Real numbers are associated with points on the x-axis For example:... read more
Complex Numbers In algebra, there are two types of numbers: real numbers and imaginary numbers. Real numbers refer to any ordinary number (e.g. 1, 2, 3 . . .) while imaginary numbers are . . . well . . . imaginary! They don't really exist, they are represented by a real number with the letter i next to it. For example, 3i is an imaginary number. Complex numbers are those consisting... read more