i Power

Algebra Level 2

Calculate the 3 6 th 36^{\text{th}} power of the square root of − 1 -1 .


The answer is 1.

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Ameya Salankar by Ameya Salankar , 23, India

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7 solutions

Ameya Salankar
Jul 1, 2014

Notice that ι 4 = 1 \iota^4 = 1 . Also notice that 36 36 is a multiple of 4 4 .

Therefore, ι 36 = ( ι 4 ) 9 = 1 9 = 1 \iota^{36} = (\iota^4)^9 = 1^9 = \boxed{1} .

11 Helpful 0 Interesting 0 Brilliant 0 Confused

but the square root of a negative number (in this case -1) does'n exist...

Marco Faustini - 6 years, 11 months ago

@ Marco Faustini: Google the square root of -1 and a symbol "i" should appear. There should be multiple websites explaining the concept.

William Shao - 6 years, 11 months ago

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the "i" is part of the imaginary set of numbers; it essentially splits the problem into two sections - your real set of numbers (i.e. 1, which follows basic algebraic rules), and an imaginary set of numbers by which "i" is carried through the problem

kristina toope - 6 years, 10 months ago

i 36 = ( ( − 1 ) 2 ) 18 = ( − 1 ) 18 = ( ( − 1 ) 2 ) 9 = 1 9 = 1 i^{36}=((\sqrt{-1})^2)^{18}=(-1)^{18}=((-1)^2)^9=1^9=\boxed{1}

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Prince Mishra
Jul 8, 2014

because we have to calculate 36th power which is positive so ans will be 1

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Fox To-ong
Jan 13, 2015

SAME AS i^4

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Satvik Mashkaria
Jul 8, 2014

( − 1 ) 0.5 ∗ 36 = ( − 1 ) 18 = 1 (-1)^{0.5*36}=(-1)^{18}=1

1 Helpful 0 Interesting 0 Brilliant 0 Confused

36 mod 4 = 0, so must be i^36 = i^0 = 1.

Marlon Borba - 6 years, 10 months ago
Prokash Shakkhar
Dec 10, 2016

We know that, i 4 = 1 i^4 =1 .. So, ( i 4 ) 9 = 1 , → i 36 = 1 (i^4)^9 =1, → i^{36} = 1 So, the answer is 1 \boxed{1}

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Sir isaac Newton
Nov 26, 2016

( − 1 ) 36 = ( − 1 ) 18 = 1 (\sqrt {-1})^{36}= (-1)^{18}=1

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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