Please enable JavaScript.
Coggle requires JavaScript to display documents.
Introdaction Complex Number - Coggle Diagram
Introdaction Complex Number
What is it?
any number of the form a+bi
a,b E R
i= √-1
it is equel to z
a is the real part of z
written Re(z)
b is the imaginary part of z
written Im(z)
For Example
If z= 2+3i
Re(z)=2
Im(z) =3
If z= -√2i
Re(z) = 0
Im(z) = -√2
it shown as "z"
Conjugates (Eşlenik)
What is it?
changing the symbol of equation
Complex conjugate
is about changing the symbol of the imaginary part.
An example
lets say z= a+bi
Re(z)= Re(z*)
Im(z*) = -Im(z)
The Properties
somethings reverse of reverse is always equals to the original form
the parantecesis doesn't change anything in this case
because in the end you will always have the sum/difference of both conjugate values.
same thing from the previous example
both values will cancel each other
A special Property
Solving the equation of quadratics
Solution
important thing is you can multiply "√"
Solution
important thingis:
Use the quadratic formula
Equality of Complex Numbers
It is coming from the principles of math
If there is equality two side of the equation have to satisfy each other.
What is it?
Two complex numbers are equal when their real parts are equal and their imaginary parts are equal.
a +bi = c +di
a = c
b = d
extra information
for the complex number a +bi
where a and b are real numbers
a = 0
b = 0
some examples
(x + 2i) (1 -i) = 5 + yi
Solution
try the make the equation on the left simualar to the one in the right
The Sum Of Two Squares Factorisation
Normally what is it?
in this Unit
We have information of
i= √-1
but we also know
extra information
So we can say
an Example
Solution
Operations Of Complex Numbers
It is no different from functions
