plural

Retrieved from http://www.qiujiawei.com/understanding-quaternions/

 

The set of complex numbers is the sum of a real number and an imaginary number in the form:

 

It can be considered that all real numbers are complex numbers with b=0 and all imaginary numbers are complex numbers with a=0.

addition and subtraction of complex numbers

addition:

 

Subtraction:

 

Coefficient scaling of complex numbers

 

product of complex numbers

 

complex square

 

complex conjugate

Conjugation of a complex number means making the imaginary part of a complex number negative. The symbol for conjugate complex numbers is .

 

The product of a complex number and its complex conjugate is:

 

Absolute value of complex number

We use complex conjugates to compute the absolute value of complex numbers:

 

Quotient of two complex numbers

 

power of i

If the square of is equal to -1, then the nth power should also exist:

 

If you write in this order, you will get a pattern like this: (1,\mathbf i,-1,-\mathbf i,1,...)

A similar pattern also occurs with increasing negative powers:

i