fordy2707 said:
An Argand Diagram is a graphical representation of complex numbers on a two-dimensional plane. It consists of a horizontal real axis and a vertical imaginary axis. The complex number z = a + bi is represented by a point (a,b) on the plane.
To solve for $z_1^*$ on an Argand Diagram, you must first find the conjugate of the complex number z = a + bi. This is done by changing the sign of the imaginary part, resulting in z* = a - bi. Then, the point (a,b) representing z on the Argand Diagram will have a reflection across the real axis, resulting in the point (a,-b) which represents z*.
Solving for $z_1^*$ on an Argand Diagram is important in complex number operations, such as addition, subtraction, multiplication, and division. It allows us to find the conjugate of a complex number and perform these operations more easily.
Yes, you can solve for $z_1^*$ on an Argand Diagram using polar form. To do this, you must first convert the complex number from rectangular form (a + bi) to polar form (r(cosθ + isinθ)). Then, to find z*, you simply change the sign of the angle θ, resulting in r(cosθ - isinθ).
Solving for $z_1^*$ on an Argand Diagram is equivalent to finding the complex conjugate of a complex number. The complex conjugate is the number with the same real part but the opposite imaginary part. On an Argand Diagram, this is represented by reflecting the point representing the complex number across the real axis.
