# Math Help - Complex Numbers - Modulus

1. ## Complex Numbers - Modulus

My question is: Find the modulus of ((15i)^4)/((-5-10i)^6)

For this would the top line just be 15^4 = 50625.

The bottom line: root 125 then to the power 6.

2. you seem to do be doing well, know how to find the modulus of both the denominator and the numerator, now you just divide them.

3. Okay thanks, I get 50625/1953125.
This simplifies to 81/3125.

The only problem I have is that this is practice question from a non-calculator test. Do you you know if there is an easier way to approach this with no calculator. Thanks.

4. well the numbers in this question are fairly easy due to nice prime factors

$125 = 5^3$
$15= 5 \cdot 3$

$\frac{(5 \cdot 3)^4 } {(5^3)^3} \rightarrow \frac{5^4 \cdot 3^4 } {5^9} \rightarrow \frac{3^4 } {5^5}$