Answer:
-75+100i
Step-by-step explanation:
(5 + 10i)²
Using the FOIL method
((5 + 10i) (5 + 10i)
First 5*5 = 25
Outer = 5 * 10i = 50i
Inner = 10i * 5 = 50i
Last = 10i * 10i - 100i^2 = 100 (-1) = -100 (Remember that i^2 = -1)
Add these together
25 +50i+50i - 100
[tex] \pink{100 {i}^{2} + 100i + 25}[/tex]
[tex](5 + 10i)^{2} \\ (5 + 10i)(5 + 10i) \\ 5(5 + 10i) + 10i(5 + 10i) \\ 25 + 50i + 50i + 100i ^{2} \\ 25 + 100i + 100 {i}^{2} \\ \rightarrow100 {i}^{2} + 100i + 25[/tex]
