Question

what is the value of √2-3i              
tell me the simplest way to solve it

Answer 1

there is nothing called as the value of a complex number. but there is something called the absolute value of a complex number which is actually the distance of the complex number from the origin in the argand plane. the absolute value of a complex number is:-
$|a+ib|= \sqrt{a^2+b^2}$
therefore $|\sqrt{2}-3i|=\sqrt{2+9}=\sqrt{11}$

Answer 2

absolute value of 2^1/2-3i=(2^1/2^2+(-3)^2)    (since,abs. value of a+bi=(a^2+b^2))
                                    =(2+9)^1/2=11^1/2