Question

If $Z=\frac{(\sqrt{3}+i{)}^3(3i+4{)}^2}{(8+6i{)}^2}$ then $|Z|$ is equal to

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (C)

We have ,
$z=\frac{{\left(\sqrt{3}+i\right)}^3{\left(3i+4\right)}^2}{{\left(8+6i\right)}^2}$
$\Rightarrow \left|z\right|=\frac{{|\sqrt{3}+i|}^3{|3i+4|}^2}{{|8+6i|}^2}$
$=\frac{{\left(\sqrt{{\left(\sqrt{3}\right)}^2+{\left(1\right)}^2}\right)}^3{\left(\sqrt{{\left(3\right)}^2+{\left(4\right)}^2}\right)}^2}{{\left(\sqrt{8^2+6^2}\right)}^2}$
$=\frac{{\left(2\right)}^3{\left(5\right)}^2}{{\left(10\right)}^2}=2$