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For any number n>1, is

|(.5 +.2i)^n|
A. greater than 1?
B. less than 1?
C. equal to 1?
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For any number n>1, is |(.5 +.2i)^n| A. greater than 1? B. less than 1? C. equal-example-1

1 Answer

4 votes

Answer:

B. Less than 1

Explanation:

You could plug in values of n greater than 1 and see what happens....

Example n=2 gives |(.5+.2i)^2|

Simplifying inside gives |(.5)^2+2(.5)(.2i)+(.2i)^2|

=|.25+.2i+.04i^2|=|.25+.2i-.04|=|.21+.2i|.

Applying the absolute value part gives sqrt(.21^2+.2^2)=sqrt(.0441+.04)=sqrt(.0841)=.29

This value is less than 1.

We should also be able to do the absolute value first then the power.

|.5+.2i|=sqrt(.25+.04)=sqrt(.29)

So |.5+.2i|^2=.29 which is what we got long way around.

Anyways (sqrt(.29))^n where n is greater than 1 will result in a number greater than 0 but less than 1.

User Not Amused
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