(1) 4i−(3−2i)=−3+6i4i - (3 - 2i) = -3 + 6i4i−(3−2i)=−3+6i (2) 1+5i−2(−4−i)=9+7i1 + 5i - 2(-4 - i) = 9 + 7i1+5i−2(−4−i)=9+7i (3) 2(5−3i)−3(3−2i)=10−6i−9+6i=12(5 - 3i) - 3(3 - 2i) = 10 - 6i - 9 + 6i = 12(5−3i)−3(3−2i)=10−6i−9+6i=1 (4) (4−3i)(2+i)=8−2i+3=11−2i(4 - 3i)(2 + i) = 8 - 2i + 3 = 11 - 2i(4−3i)(2+i)=8−2i+3=11−2i (5) (1+i)2=1+2i−1=2i(1 + i)^2 = 1 + 2i - 1 = 2i(1+i)2=1+2i−1=2i (6) (2−i)(3+2i)=32−i+2=42−i(\sqrt{2} - i)(3 + \sqrt{2}i) = 3\sqrt{2} - i + \sqrt{2} = 4\sqrt{2} - i(2−i)(3+2i)=32−i+2=42−i (7) 2i=−2i\frac{2}{i} = -2ii2=−2i (8) 6+4i5−i=(6+4i)(5+i)(5−i)(5+i)=30+26i−425+1=26+26i26=1+i\frac{6 + 4i}{5 - i} = \frac{(6 + 4i)(5 + i)}{(5 - i)(5 + i)} = \frac{30 + 26i - 4}{25 + 1} = \frac{26 + 26i}{26} = 1 + i5−i6+4i=(5−i)(5+i)(6+4i)(5+i)=25+130+26i−4=2626+26i=1+i