Complex Conjugate
To find the complex conjugate of a number just change the sign. Click below and get used to the idea
Division of Complex Numbers
Complex conjugates are used in the division of complex numbers
Find 
1+4i

in the form a + bi  
2i


1+4i

=

(1+4i)(2+i)  Multiplying the top and bottom by the complex conjugate of the bottom is the same as multiplying by 1 so it does not change the value just the form.  
2i

(2i)(2+i)  
=

2+i+8i+4i2  
4+2i2ii2  remember i2 = 1 
=

2+9i4  the 2i2i cancelled each other out  
4(1)  
Solution  
2 + 9i  
05 0 5 