Question

(Ch.- Complex no. and Quadratic Eq.)

>> i^61= ?

{Answer with process..! }

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Answer 1

Question:-

$\rm \iota^{61}$

Answer:-

$\rm \\\\: \iota^{61}$

$\rm = (\iota^{4})^{15} \iota$

now we know that i² =- 1

$\rm \iota^{2^{2}} = -1^{2}$

$\rm = \iota^4 = 1$

$\rm = 1^{15} \iota$

$\rm = 1 \iota$

$\rm = \iota$

$\rm = \sqrt{-1}$

$\rm$

Additional Information:-

Complex number:- A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i represents the imaginary unit, satisfying the equation i² = −1. Because no real number satisfies this equation, i is called an imaginary number.