Question

Find the modulus of $\frac{\left(1+3i\right)\left(2-5i\right)}{\left(2-\sqrt{6}i\right)\left(-3+2\sqrt{5}i\right)}$

Answer 1

modulus of $\frac{(1+3i)(2-5i)}{(2-\sqrt{6}i)(-3+2\sqrt{5}i)}=\frac{|1+3i||2-5i|}{|2-\sqrt{6}i||-3+2\sqrt{5}i|}$

$=\frac{\sqrt{1}0\sqrt{2}9}{\sqrt{1}0\sqrt{2}9}$

$=\frac{1}{1}=1$