Question

Find the modulus of (3+2i)^3

Answer 1

Answer:

$13^{3/2} = \sqrt{13^3} \approx 46.87$

Step-by-step explanation:

The modulus of $z$ is $\sqrt{z\bar z}$ where $\bar z$ is the conjugate of $z$.

Here we have $z = (3+2i)^3$.

The conjugate is then $\bar z = (3-2i)^3.$

Taking the product gives

      $z\bar z = (3+2i)^3(3-2i)^3 = \bigl(3^2-(2i)^2\bigr)^3=(9+4)^3=13^3.$

The modulus is then the square root of this, so it is $13^{3/2}$.

Hope this helps you out.