Question

find the modulus of (5+4i)⁴​

Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

MODULUS OF COMPLEX NUMBER

For any complex number z = x + iy the modulus of the complex number z is denoted by | z | and defined as :

$|z| = + \sqrt{ {x}^{2} + {y}^{2} }$

FORMULA TO BE IMPLEMENTED

For any complex number z

$| {z}^{n} | = { |z| }^{n}$

EVALUATION

Here z = 5 +4i

So

$|z|$

$= \sqrt{ {5}^{2} + {4}^{2} }$

$= \sqrt{25 + 16}$

$= \sqrt{41}$

Therefore

$| \: ({5 + 4i}^{4} )|$

$= { |5 + 4i| }^{4}$

$= {( \sqrt{41} )}^{4}$

$= 1681$