Correct Answer - Option 4 : 6√6
Concept:
The modulus of a complex number is the distance of the complex number from the origin in the argand plane.
If z = x + iy is a complex number where x and y are real and i = √-1,
Then the non-negative value \(\sqrt{x^2+y^2}\) is called the modulus of complex number z (or x + iy).
The modulus of a complex number is also called the absolute value of the complex number.
Calculation:
We have,
z = (5 + √-11)(1 + √-5) = (5 + √11i)(1 + √5i)
Now, let v = (5 + √11i) and w = (1 + √5i)
\(\Rightarrow \left | v \right |= \sqrt{5^2+(√{11})^2}=\sqrt{25+11}=6\)
\(\Rightarrow \left | w \right |= \sqrt{1^2+(√{5})^2}=\sqrt{1+5}=√6\)
Modulus of the complex number z is given by
\(\left | z \right |=\left | vw \right |=\left | v \right |\left | w \right |\)
\(\therefore \left | z \right |=6\sqrt{6}\)
Hence, the modulus is 6√6.
