5/(2+4i) simplifies to (1-2i)/2.
Let's start by simplifying the expression 5/(2+4i). To do this, we need to rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator. The conjugate of 2+4i is 2-4i.
Multiplying the numerator and denominator by the conjugate:
5/(2+4i) = (5*(2-4i))/((2+4i)*(2-4i))
Expanding the denominator:
(5*(2-4i))/(2*2 + 2*(-4i) + 4i*2 + 4i*(-4i))
Simplifying:
(5*(2-4i))/(4 + 16)
(5*(2-4i))/20
(1/4)*(2-4i)
Now let's simplify the expression (1-2i)/2:
(1-2i)/2 = 1/2 - (2i/2) = 1/2 - i
Comparing the results:
(1/4)*(2-4i) = 1/2 - i
The two expressions are equal, so we can say that 5/(2+4i) is equal to (1-2i)/2.