3 + 2i + (6 + i)(5 + i)

= 3 + 2i + (6.5 – 1.1) + (6.1 + 5.1).i

= 3 + 2i + 29 + 11i

= 32 + 13i.

(3 - 2i)(2 - 3i) = 3. 2 – 3. 3i - 2i.2 - 2i. (- 3i) = 6 – 9i – 4i – 6 = ( 6- 6) + ( -9 – 4).i = -13i

2 + i + 1 + i 4 - 3 i 3 + 2 i = 31 13 - 12 13 i

a) 54 – 19i;

b) -15 + i.

3 - 4 i 1 + 2 i 1 - 2 i + 4 - 3 i = 27 5 + 9 5 i

\(\frac{\left(2-3i\right)\left(4-i\right)}{3+2i}\)

\(=\frac{8-2i-12i+3i^2}{3+2i}=\frac{5-17i}{3+2i}=\frac{\left(5-17i\right)\left(3-2i\right)}{\left(3+2i\right)\left(3-2i\right)}\)

\(=\frac{15-10i-51i+34i^2}{9-4i^2}=\frac{-19-61i}{9+4}=\frac{-61i-19}{13}\)