Question

Perform the indicated operation and express the result as a simplified complex number in the form a+bi. Do not put any spaces between your characters.(2-3i)-(3+2i)simplifies to Answer

Answer 1

To determine the simplified complex number in the form a+bi :

`(2-3i)-(3+2i)`

The standard symbol for the set of all complex numbers is C, and we'll also refer to the complex plane as C.

We'll try to use x and y for real variables, and z and w for complex variables. For example, the equation z = x + yi is to be understood as saying that the complex number z is the sum of the real number x and the real number y times i. In general, the x part of a complex number z = x + yi is called the real part of z, while y is called the imaginary part of z. (Sometimes yi is called the imaginary part.)

When we use the xy-plane for the complex plane C, we'll call the x-axis by the name real axis, and the y-axis we'll call the imaginary axis.

`\begin{gathered} (2-3i)-(3+2i) \\ 2-3i-3-2i \\ 2-3-3i-2i \\ -1-5i \end{gathered}`

Hence the simplified complex number are in the form: = -1 - 5i

`a+bi\equiv\text{ -1-5i}`