z is a general complex number. It's often represented if the xy-plane (the Argand plane) by letting x be the real part of z and letting y be the imaginary part of z, i.e. z = x + jy, where x & y are real variables.polaris90 said:sketch the line described by the equation |z - u| = |z|
u = -1 + j√3
I don't understand how to do this. I'm not sure of what z is exactly. Can anybody explain to me what it is?
On a graph, the imaginary part of a complex number is typically represented on the y-axis, and the real part is represented on the x-axis. The point where these two axes intersect is the origin (0,0). The complex number is then plotted as a point on the graph, with its real and imaginary parts corresponding to the x and y coordinates, respectively.
The slope of a line passing through two complex numbers, z1 and z2, can be found using the formula:
m = (Im(z2) - Im(z1)) / (Re(z2) - Re(z1))
where Im(z) represents the imaginary part of the complex number and Re(z) represents the real part.
To sketch a line using polar coordinates, first convert the complex numbers to polar form. Then, plot the points on a polar coordinate system using the magnitude as the distance from the origin and the argument as the angle. Connect the points to form the line.
Yes, it is possible to sketch a line passing through three or more complex numbers. Simply follow the same steps as you would for two complex numbers, plotting each point on the graph and connecting them to form the line.
Yes, there is a faster way to sketch a line from complex numbers. You can use the vector addition and scalar multiplication properties of complex numbers to find additional points on the line. Plot these points on the graph and connect them to form the line.