Question

The product of the four values of the complex number $(1+i)^{3/4}$ is

• A. $2(1+i)$
• B. $2(1-i)$
• C. $2^3 (1+i)$
• D. $2^3 (1-i)$

Hint:

Remember the product of roots of unity or complex roots has specific formulas based on root order and powers.

Answer 1

The Correct Option is B

The four values of $(1+i)^{3/4}$ are the four 4th roots of $(1+i)^3$. The product of all roots of an equation $x^n = a$ is $a$ if $n$ is even. Simplifying gives the product as $2(1 - i)$.