(1+(2*I))/(3-(4*I))+2/5
WRONG!
From ( -5 + 10*I )/25 + 2/5, I get
(1 + 2i)/5
To simplify this expression, we need to get rid of the complex denominators. To do this, we multiply the first term by the complex conjugate of the denominator and the second term by a fraction that is equivalent to 1 but has a real denominator of 5:
(1+(2*I))/(3-(4*I)) * (3+(4*I))/(3+(4*I)) + 2/5
= (3 + 10*I - 8)/(9 + 16) + 2/5
= ( -5 + 10*I )/25 + 2/5
= (-1 + 2*I)/5
Therefore, (1+(2*I))/(3-(4*I))+2/5 simplified is (-1 + 2*I)/5.