Simplify (10+5i) / (2-i)

10+5i/2-i

=3+4i

if you take out the parenthesis

1. Rationalise the denominator

(20+10i+10i-5) / 2^2-i^2

2. Collect like terms

((20-5) + (10i+10i)) / 2^2-i^2

3. Simplify (20-5) + (10i+10i) to 15+20i

15+20i/2^2-i^2

4. Simplify 2^2 to 4

15+20i/4-i^2

5. Use square rule

15+20i/4 - (-1)

6. Simplify brackets

15+20i/4+1

7. Simplify 4+1 to 4

15+20i/5

8. Factor out the common term 5

5 (2+4i) / 5

9. Cancel 5

3+4i

10. Your final answer

3+4i

Have a nice day; D