(y-1)^2=0 is this correct?
how would I go about the Im(2iz) LHS on the first equation?
And if (y-1)2= 0, what can you say about y?gaborfk said:Homework Statement
Describe the locus of points z satisfying the given equation.
Homework Equations
Im(2iz)=7
|z-i|=Re(z)
The Attempt at a Solution
I started on the second one:
I think that Re(z) is just x, then
I squared both sides, simplified and got
(y-1)^2=0 is this correct?
Pretty much the same thing. Let z= x+iy. What is 2iz in terms of x and y? What is Im(2iz)?If so how would I go about the Im(2iz) LHS on the first equation?
Thank you
Complex numbers are numbers that consist of a real part and an imaginary part, represented as a + bi, where a and b are real numbers and i is the imaginary unit. In geometry, complex numbers are represented as points on a two-dimensional plane, with the x-coordinate representing the real part and the y-coordinate representing the imaginary part.
In geometry, addition and subtraction of complex numbers are performed by adding or subtracting the real and imaginary parts separately. Multiplication of complex numbers is done by using the distributive property, and division is done by multiplying the complex number by its conjugate.
The modulus of a complex number is its distance from the origin on the complex plane, and the argument is the angle it makes with the positive real axis. This can also be thought of as the magnitude and direction of the complex number in polar form.
Complex numbers are used to represent transformations such as translations, rotations, reflections, and dilations in the complex plane. These transformations can be visualized and computed using complex number operations.
Yes, complex numbers can be used to solve geometric problems such as finding the coordinates of points, determining the distance between points, and finding the equations of lines and circles on the complex plane.