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Algebra Level 2

( i ) 4 = ? \Large\left (\sqrt{i} \right)^4 = \, ?

Clarification : i is a complex number

1 1000 57 67 -1 2 6 3

Gourab Roy by Gourab Roy , 20, India

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4 solutions

Atul Shivam
Jan 14, 2016

( i ) 4 = i 2 = − 1 (\sqrt{i})^4=i^2=\boxed{-1}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Just wondering, why it can't be?

( i ) 4 = i 4 = 1 = 1 {\left( \sqrt{i} \right)}^4 = \sqrt{i^4} = \sqrt{1} = 1

Tapas Mazumdar - 4 years, 2 months ago

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Bro i i is not a real number we cant simply apply equations of real number here, it has some restrictions

Atul Shivam - 4 years, 2 months ago
Kay Xspre
Jan 14, 2016

( i ) 4 = i 4 2 = i 2 = − 1 \large(\sqrt{i})^4 = i^{\frac{4}{2}} = i^2 = -1

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Just wondering, why it can't be?

( i ) 4 = i 4 = 1 = 1 {\left( \sqrt{i} \right)}^4 = \sqrt{i^4} = \sqrt{1} = 1

Tapas Mazumdar - 4 years, 2 months ago
. .
May 16, 2021

i 1 2 4 = i 2 = − 1 { i ^ { \frac { 1 } { 2 } } } ^ { 4 } = i ^ { 2 } = -1 .

0 Helpful 0 Interesting 0 Brilliant 0 Confused

( i ) 4 = ( i 1 2 ) 4 = i 2 = \large{(\sqrt{i})^4=\left(i^{\frac{1}{2}}\right)^4=i^2=} − 1 \large{\boxed{-1}}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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