Question

The value of i 215×−i 215  is​

Answer 1

Answer:

the value of I 215 ×i-215 is

Answer 2

The value of $i^{215}\times-i^{215}$ is 1.

Step-by-step explanation:

Given: $i^{215}\times-i^{215}$

To find: The value of above expression

• We know, the following rule for $iota\ (i)$:

        $i^{4n}=1 \\i^{4n+1}= i\\i^{4n+2}=-1\\i^{4n+3}=-i$

• Therefore, through this method, we can find the value of $i^{215}$. Also, 215 is not a multiple of 4 and leaves 3 as remainder.

      ⇒ $i^{215}= i^{212+3$

      ⇒ $i^{215}=i^{4\times53+3}$

      ⇒ $i^{215}= i^{4n+3$

      ⇒ $i^{215}=-i$

• Thus, the given expression becomes:

      ⇒ $-i\times-(-i)$

      ⇒ $-i\times i$

• Since, $i^{2} = -1$,

      ⇒  $-(-1) =1$

Hence, The value of $i^{215}\times-i^{215}$ is 1.