Powers of i repeat in a cycle of 4i की घातें 4 के चक्र में दोहराती हैंPowers of i repeat in a cycle of 4

Section 4.3.5 · Class 11 Maths Ch 4 · interactive diagram

Parts and what they mean

• i⁴ = 1 (i⁴ = 1) — i^(4k) = 1 for every integer k.
• i¹ = i (i¹ = i) — i^(4k+1) = i.
• i² = −1 (i² = −1) — i^(4k+2) = −1. This is the definition of i.
• i³ = −i (i³ = −i) — i^(4k+3) = −i.
• Multiply by i = quarter turn (i से गुणा = चौथाई घुमाव) — To find iⁿ, divide n by 4 and use the remainder. Example: i¹⁹ → remainder 3 → −i.

Original diagram drawn by Simple Learning Hub for NCERT Class 11 Maths Ch 4. Report a mistake