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Find \(\left|\left(\frac 35+\frac 45i\right)^6\right|\)

 Mar 4, 2021
 #1
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Multiplying this out the long way is tedious, put will give you the correct answer.

 

You can use the shortcut:  (x + y)6  =  x6 + 6x5y + 15x4y2 + 20x3y3 + 15x2y4 + 6xy5 + y6

where  x = 3/5  and  y = 4/5·i.           (You can get the coefficients by using either combinations, or Pascal's triangle.)

 

Finally, find the absolute value of the answer.

 Mar 4, 2021
 #2
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Geno maybe that is magnitude?

 Mar 4, 2021

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