Complex Numbers - Modulus

**haku** · December 16th 2007, 04:03 AM

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.

Please help. Thanks

**bobak** · December 16th 2007, 04:29 AM

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.

**haku** · December 16th 2007, 05:07 AM

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.

**bobak** · December 16th 2007, 05:20 AM

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

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

so your fraction is

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

so this can be done fairly easily without a calculator

**haku** · December 16th 2007, 05:22 AM

Thanks for your help

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