P is similar to _i_

Algebra Level 3

If P= − 1 \sqrt{-1} , then find ( 1 − P ) 20 (1-P)^{20}


The answer is -1024.

Manish Mayank by Manish Mayank , 20, India

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3 solutions

Manish Mayank
May 28, 2014

Try it your self!!! (dont think i dont know the soln)

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I admire you, your problems are awesome

Iancarlo Espinosa - 7 years ago

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So pls share my posts because they dont reach much people

Manish Mayank - 7 years ago

( 1 − P ) 20 = ( ( 1 − P ) 2 ) 10 = ( 1 − 2 P + ( − 1 ) ) 10 = ( 2 P ) 10 (1-P)^{20}=((1-P)^2)^{10}=(1-2P+(-1))^{10}=(2P)^{10} Separating the power,we have: 2 10 × P 10 2^{10}\times P^{10} 1024 × ( − 1 ) 2 ) 5 1024\times(\sqrt{-1})^2)^5 1024 × ( − 1 ) 5 = − 1 × 1024 = − 1024 1024\times(-1)^5=-1\times1024=\boxed{-1024}

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John Kamel
Aug 18, 2014

(1-i)^20 =root 2 (cos315+isin 315)=1024 -1

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