For a complex number $z$, let $(1+z)^{15}=a_0+a_1 z+\cdots+a_{15} z^{15}$. The value of
$\left(a_0-4 a_2+16 a_4+\cdots-2^{14} a_{14}\right)^2+\left(2 a_1-8 a_3+32 a_5 \cdots-2^{15} a_{15}\right)^2$ is

• A

  $2^{30}$
• B

  $2^{15}$
• C

  $1$
• Correct answer
  D

  $5^{15}$

Hence, the correct answer is option: 'D'.