How to solve below equation ?

Question

The value of $\frac{(1-i\sqrt 3)^{30}}{ (1+i)^{60}} \left( i = \sqrt {-1}\right)$ is ______.

• A. 1
• B. 0
• C. -1
• D. 2

Answer 1

$\frac{(1-i\sqrt 3)^{30}}{ (1+i)^{60}}\\
=\frac{(1-2i\sqrt 3-3)^{15}}{(1+2i-1)^{30}}\\
=\frac{(-2-2i\sqrt 3)^{15}}{(2i)^{30}}\\
=\frac{(-2)^{15}(1+i\sqrt 3)^{15}}{(2i)^{30}}\\
=\frac{(-1)^{15}(2)^{15}(1+i\sqrt 3)^{15}}{(-1)(2)^{30}}\\
=\frac{(1+3i\sqrt 3-9-3i\sqrt 3)^5}{2^{15}}\\
=\frac{(-8)^5}{2^{15}}\\
=-1$

Comments

Remove extra spaces below, ur answer will look better  :)

Answer 2

option c

-1 is right ans .

very simple but lengthy

do it by simplification

first break both square form

than break numerator in qubic for it will easily crack the qus

Comments

complex number is in syllabus ?