Question

Find the value of (5 + 10i)² ​

Answer 1

`\pink{100 {i}^(2) + 100i + 25}`

Explanation:

`(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`

Answer 2

-75+100i

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

-75+100i