Answer:
[tex]1) \dfrac{12+\sqrt{-16}}{4}=\dfrac{12+\sqrt{16i^{2}}}{4}\\\\\\=\dfrac{12+4i}{4}=\dfrac{12}{4}+\dfrac{4i}{4}\\\\\\= 3 + i[/tex]
Real part = 3 & imaginary part = 1
2) 4 + 7i - 8 = 4 -8 + 7i
= -4 + 7i
Real part = -4 & imaginary part = 7
[tex]3)\dfrac{\sqrt{9}+\sqrt{-4}}{5}=\dfrac{3+\sqrt{4i^{2}}}{5}\\\\\\=\dfrac{3}{5}+\dfrac{2i}{5}\\\\\\Real \ part = \dfrac{3}{5} \ & \ imaginary \ part = \dfrac{2}{5}[/tex]
[tex]4) -2-\sqrt{-25}=-2-\sqrt{25i^{2}}=-2-5i[/tex]
Real part = -2 & imaginary part = -5
[tex]5)\dfrac{15-13i}{3}=\dfrac{15}{3}-\dfrac{13i}{3}\\\\\\Real \ part = \dfrac{15}{3} \ & \ imaginary \ part = \dfrac{-13}{3}[/tex]
b) 1) 6 + 4i
2) -12+ 5i
3) 5-14i
