Question

Evaluate (i¹³¹ + i⁴⁹)

Answer 1

Answer:

0

Step-by-step explanation:

Hi,

We know that i² = -1

and i³ = i²*i = -1*i = -i

and i⁴ = (-1)² = 1

Consider i¹³¹ = i¹²⁸⁺³

= i¹²⁸*i³

= (i⁴)³²*i³

= (1)³²*(-i)

= -i

Consider i⁴⁹ = i⁴⁸⁺¹

= i⁴⁸*i

= (i⁴)¹²*i

= (1)¹²*i

= i

Consider i¹³¹ + i⁴⁹

= -i + i

= 0.

Hope, it helps !

Answer 2

$\texttt \green { Solution }$

$\textsf \red { Given }$

$\left ( i^{131} + i^{49} \right )$

= $( \left ( i^{130} \cdot i \right ) + i^{48} \cdot i \right )$

= $i\Big (\left ( i^{2}\right )^{65} + \left ( i^{2}\right )^{24} \Big)$

= $i\Big ( \left (-1 \right )^{65} + \left ( -1 \right )^{24} \Big )$

= $i \cdot ( -1 + 1 )$

= $ i × 0 $

= $ 0 $

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