Выполните действие ((5+2i)/(2-5i))-((3-4i)/(4+3i))

[latex]\frac{5 + 2i}{2 - 5i} - \frac{3 - 4i}{4 + 3i} = \frac{(5 + 2i)*(4 + 3i)-(3 - 4i)*(2 - 5i)}{(2 - 5i)*(4 + 3i)}=\\ \\ = \frac{(20 + 15i + 8i + 6*(-1)) -(6 -15i - 8i+20*(-1))}{8 +6i-20i-15*(-1)} = \\ \\ = \frac{(20 + 23i - 6) - (6 - 23i - 20)}{23 - 14i} = \frac{14 + 23i - (-14 - 23i)}{23 - 14i} = \\ \\ \frac{14 + 23i + 14 + 23i}{23 - 14i} = \frac{2 * (23i + 14)}{23 - 14i} = \frac{2*i*(23 - 14i)}{23 - 14i} = 2i [/latex]