Verified answer

(5i − 2i) / (1−2i) . .. multiply top and bottom by 1 + 2i

(5i − 2i)(1+2i) / (1-2i)(1+21)

= [ (5i)(1) + (5i)(2i) - 2i(1) - 2i(2i) ] / [ 1 - (2i)^2 ]

note: i = √-1

= [ 5i + 10i^2 - 2i - 4i^2 ] / [1 - 4i^2]

= [ 3i -10 + 4 ] / [ 1 + 4 ]

= (3i - 6) / (5)

hence, (-6/5) + (3/5)i

(5i-2i)(1+2i)/5

= 5i-10-2i+4/5

= 3i-6/5

(5i - 2i) / (1 - 2i) =>

3i / (1 - 2i) =>

3i * (1 + 2i) / ((1 - 2i) * (1 + 2i)) =>

(3i + 6i^2) / (1 - 4i^2) =>

(3i - 6) / (1 + 4) =>

3 * (i - 2) / 5 =>

(3/5) * (i - 2)

(5i - 2i)/(1 - 2i) = (3i)/(1 - 2i) = (3i)(1 + 2i) = (3i)(1 - 2i)/(1 - 4i²) = (3i)(1 - 2i)/5 = (3i + 6)/5

(5 − 2i) / (1 − 2i) = (5 − 2i)(1 + 2i) / (1 − 2i)(1 + 2i)

. . . . . . . . . . . . = (5 + 10i − 2i − 4i²) / (1 − 4i²)

. . . . . . . . . . . . = (5 + 8i + 4) / (1 + 4)

. . . . . . . . . . . . = (9 + 8i) / 5