Question

Simplify:$(\sqrt{3}+i\sqrt{2})(\sqrt{2}+i\sqrt{3})$

• A. $2\sqrt{6}+5i$
• B. $2\sqrt{6}-5i$
• C. 5i
• D. -5i

Answer 1

The correct option is C 5i

Let $Z=(\sqrt{3}+i\sqrt{2})(\sqrt{2}+i\sqrt{3})$

$=\sqrt{3}(\sqrt{2}+i\sqrt{3})+i\sqrt{2}(\sqrt{2}+i\sqrt{3})$

$=\sqrt{6}+3i+2i+i^2\sqrt{6}$

$=\sqrt{6}+3i+2i-\sqrt{6}$

$Z=5i$