1. Tardigrade
  2. Question
  3. Mathematics
  4. (√[3]3+(35 / 6) i)3 is an integer where i=√-1. The absolute value of the integer is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. $\left(\sqrt[3]{3}+\left(3^{5 / 6}\right) i\right)^{3}$ is an integer where $i=\sqrt{-1}$. The absolute value of the integer is equal to

Complex Numbers and Quadratic Equations

Solution:

Solving, $\left[3^{1 / 3}(1+\sqrt{3} i)\right]^{3}=3(1+\sqrt{3} i)^{3}$
$=3 \cdot 8\left(\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}\right)^{3}=-24$