Similarly Joe can divide the complex number 2i by 12i and wr

Similarly, Joe can divide the complex number 2-i by 1+2i, and write the result in the form a+bi. Joe sets up the division as a fraction: 2-i/1+2i=a+bi what are the values of a and b?

Solution

(2- i)/(1+2i)

rationalise the denominator by multiplying with ( 1-2i) in num and den.

(2-i)( 1- 2i)/( 1- (2i)^2)

= ( 2 -4i - i -2)/( 1+4)

= ( -5i)/5

= -i

In the form a+bi = 0 - i

a=0 ; b =-1