What did you do?
These look straightforward.
(1) Use the quadratic formula to solve these equations; express the answers as complex numbers.
(a)
(b)
I have more of these but I will try them on my own after I receive help on these.
The number x is called the real part of z and is writtern x = Re z. The number y, despite the fact that it is also a real number, is called the imaginary part of z and is writter y = Im z.
(2) Find Re(1/z) and Im(1/z) if z= x + iy, z . Show that Re(iz)= -Im z and Im(iz) = Re z.
If further explanation is needed, please let me know. Thanks for the help!
You know that
looks like a lot .
So write : . Here is your quadratic formula
Just use the discriminant method.(b)
In ,
Here, I'm pretty sure and this is where imaginary part intervenes.
The number x is called the real part of z and is writtern x = Re z. The number y, despite the fact that it is also a real number, is called the imaginary part of z and is writter y = Im z.
(2) Find Re(1/z) and Im(1/z) if z= x + iy, z\not=0.
When you have a complex number in a denominator, you often have to multiply it by its conjugate (called ), that is and by using the quadratic formula , we get , which is a real number.
So
Can you go from here ?
What is i*z ?Show that Re(iz)= -Im z and Im(iz) = Re z.
What do you conclude ?
You gotta be able to do these (in a first time, to "know"), because it's quite a basis of the manipulation of complex numbers...