Question

Express in the form A + iB

$\frac{(a+i{)}^2}{(a-i)}-\frac{(a-i{)}^2}{(a+i)}$

• A. $0+\frac{i(3a^2-1)}{(a^2+1)}$
• B. $0+\frac{2i(3a^2-1)}{(a^2+1)}$
• C. $0+\frac{i(3a^2+1)}{(a^2+1)}$
• D. $0+\frac{2i(3a^2+1)}{(a^2+1)}$

Answer 1

The correct option is B $0+\frac{2i(3a^2-1)}{(a^2+1)}$

$\frac{(a+i{)}^2}{(a-i)}-\frac{(a-i{)}^2}{(a+i)}=\frac{{(a+i)}^3-{(a-i)}^3}{a^2+1}=\frac{2(i^3+3a^{2}i)}{a^2+1}=\frac{2i(3a^2-1)}{a^2+1}$
Ans: B