Question

(3+i)^2 = c+di, find the value of d.

a. 1
b. 2
c. 4
d. 6
(please show work)

Answer 1

d.
`\displaystyle 6`

Explanation:

`\displaystyle [3 + i]^2 = [3 + i][3 + i] = 9 + 6i + i^2 → 9 + 6i - 1 → 6i + 8`

Therefore, the d-value is 6.

Extended Information on the Complex Number System

`\displaystyle √(-1) = i \\ -1 = i^2 \\ -i = i^3 \\ 1 = i^4\:[every\:multiple\:of\:4]`

I am joyous to assist you anytime.