Question

Evaluate the following expressions a) (3 + 2i) - (8 - 5i) b) (4 - 2i)*(1 - 5i) c) (- 2 - 4i) / i d) (- 3 + 2i) / (3 - 6i)​

Answer 1

a) 3 - 8 + 2i - (-5i) = -5 + 2i +5i = -5 + 7i

b) 4 - 20i - 2i + 10i² = 4 - 22i + 10(
`√(-1)`)² = 4 - 22i + 10(-1) = 4 - 10 -22i

= -6 -22i

c) Multiply both numerator and denominator by i

`(i(-2-4i))/(i^(2) )` =
`(-2i - 4i^(2) )/(i^(2) )` =
`(-2i - 4(√(-1))^(2) )/((√(-1))^(2))` =
`(-2i - 4(-1))/(-1)` =
`(-2i+4)/(-1)` = 2i - 4 = -4 + 2i

d) Multiply both numerator and denominator by (3+6i)

`((3+6i)(-3+2i))/((3+6i)(3-6i))` =
`(-9+6i-18i+12i^(2) )/(9-36i^(2) )` =
`(-9-12i+12(√(-1) )^(2) )/(9-36(√(-1) )^(2) )` =
`(-9-12i+12(-1))/(9-36(-1))` =
`(-9-12-12i)/(9+36)`

=
`(-21-12i)/(45)` =
`-(21)/(45) - (12)/(45)i`