Find the multiplicative inverse of the complex number 4 - 2i.

To find the multiplicative inverse of the complex
number.

We know the multiplication identity element of the complex
number (x+yi) = e(x+iy) .

 Therefore xe = x and  and xi*e = xi.
Therefore e = 1.

Therfore if the  multiplicative inverse of  4-2i is
x+yi, then

(4-2i)(x+yi) = 1.

4x+4yi-2xi
-2yi^2 = 1+0*i

4x +(4y-2x)i +2y =
1+0*i.

(4x+2y) +(4y-2x)i =
1+0*i.

Equate imaginary parts and equate real parts both
sides:

Imaginary parts: 4y -2x =
0.....(1)

Real Parts: 4x+2y =
1.....(2)

From (1): 4y- 2x = 0.

 x= 2y.
Substitute x= 2y in eq (2):

4(2y) +2y =
1

10y = 1.

y =
1/10.

x =2y= 2/10.

Therefore (4-2i) has
the multiplicative inverse  2/10+i/10.

4y + 2(2y)
=