- #1
Mathematicsss
Homework Statement
:[/B]Sketch in an argand diagram:
|z − i| = 2
Homework Equations
z= a+bi
The Attempt at a Solution
|z − i| means that the distance from z to i is 2, however I am not sure where to put z.
Mathematicsss said:Homework Statement
:[/B]
Sketch in an argand diagram:
|z − i| = 2
Homework Equations
z= a+bi
The Attempt at a Solution
|z − i| means that the distance from z to i is 2, however I am not sure where to put z.
There is not just a single location for z -- it is arbitrary. Follow Ray's advice in locating i.Mathematicsss said:|z − i| means that the distance from z to i is 2, however I am not sure where to put z.
To plot complex numbers on an Argand Diagram, you need to use the real and imaginary axes. The horizontal axis represents the real part of the complex number, while the vertical axis represents the imaginary part. The complex number is then plotted as a point on the diagram, with the real part being the x-coordinate and the imaginary part being the y-coordinate.
An Argand Diagram is used to visually represent complex numbers. It allows us to see the relationship between the real and imaginary parts of a complex number and interpret them geometrically. This diagram is especially useful in visualizing and solving complex mathematical equations and problems.
To draw a vector on an Argand Diagram, you need to first identify the starting and ending points of the vector. The starting point represents the initial value of the complex number, while the ending point represents the final value. Then, draw a line connecting the two points on the diagram to create the vector.
Yes, an Argand Diagram can be used to plot multiple complex numbers. Each complex number will be represented as a point on the diagram, and you can connect these points to visualize their relationships. This can be particularly helpful when solving systems of equations involving complex numbers.
An Argand Diagram can be used to find the modulus and argument of a complex number by using the Pythagorean theorem and trigonometric functions. The modulus of a complex number is the distance from the origin to the point representing the complex number, while the argument is the angle between the positive real axis and the vector representing the complex number.