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Algebra Level 2

Evaluate i 51 i^{51}

− i -i i i 1 1 − 1 -1

Swapnil Das by Swapnil Das , 20, India

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5 solutions

i 51 = i 3 × i 48 = [ ( − 1 ) × i ] × 1 = − i i^{51}=i^{3}\times i^{48} = [(-1)\times i] \times 1 = \boxed{-i}

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Sai Ram
Sep 6, 2015

i 51 = i 50 × i = ( i 2 ) 25 × i = − 1 × i = − i i^{51} = i^{50} \times i = (i^2)^{25} \times i = -1 \times i = \boxed{-i}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Good solution. Up voted!

Nihar Mahajan - 5 years, 9 months ago

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Thanks for the compliment.

Sai Ram - 5 years, 9 months ago

Good solution.Up voted

Rama Devi - 5 years, 9 months ago
Md Omur Faruque
Aug 28, 2015

We know that, i 4 = 1 i^4=1 . ∴ i 51 = i 48 × i 3 = ( i 4 ) 12 × i 3 = 1 × i 3 = − i \therefore i^{51}=i^{48}\times i^3=(i^{4})^{12} \times i^3=1\times i^3=\color{#0C6AC7}{\boxed {-i}}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

i 51 = i 51 ≡ 3 ( M o d 4 ) = i 3 = − i . \Large i^{51}=i^{51\equiv3 (Mod ~4)}=i^3=- ~i.

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Uahbid Dey
Aug 26, 2015

i⁵¹ = i⁴⁸⁺³ = (i⁴)¹² x i³ = 1¹² x i x i² = -i

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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