​ Find the modulus of each of the following: (3+2i)^2/(4-3i) ​

Question

Find the modulus of each of the following:

\(\frac{(3+2i)^2}{(4-3i)}\)

(3+2i)²/(4-3i)

Answer 1

Given : \(\frac{(3+2i)^2}{(4-3i)}\)

Firstly, we calculate \(\frac{(3+2i)^2}{(4-3i)}\) and then find its modulus

Now, we rationalize the above by multiplying and divide by the conjugate of 4 + 3i

Now, we have to find the modulus of

Hence, the modulus of \(\frac{(3+2i)^2}{(4-3i)}\) is \(\frac{13}{5}\)