Question

Single ( FINAL ANSWER ) Values of - iota power 5 ,iota power 6, iots power 7, iota power 8 , iota power 9 .

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Answer 1

Heya....

●(-¡)^5=1

●(¡)^6=1

●(¡)^7=-1

●(¡)^8=1

●(¡)^9=-1

@skb

Answer 2

Explanation:

• In the concept of complex numbers, any value that comes as the square root of a negative number is an imaginary complex number.

• For example, $\sqrt{-10}$ , $\sqrt{\frac{-3}{4} }$ etc are imaginary numbers and whose values cant be calculated.

• For these numbers, a value called iota $(i)$ is used. The value of iota is $\sqrt{-1}$ .

• For example, a number is written as

        $\sqrt{-10}=\sqrt{10$ × $\sqrt{-1}=10i$

From this information,

We get,

$i=\sqrt{-1}$

$i^{2}= \sqrt{-1}$ × $\sqrt{-1}$ = $-1$

$i^{3} =i^{2}.i =-1$ × $i$ $=-i$

$i^{4} =(i^{2}) ^{2}=(-1)^{2} =1$

Now, According to the question,

• $-i^{5}$

       $-i^{5}=-i^{4}.i$   $=-(1)i$

                            $=-i$  

• $i^{6}$

       $i^{6}=i^{4} .i^{2}$   $=(1)(-1)$

                        $=-1$

• $i^{7}$

      $i^{7}=i^{4} .i^{2}. i$   $=(1)(-1)i$

                         $=-i$

• $i^{8}$

       $i^{8}=i^{4}. i^{4}$   $=(1)(1)$

                        $=1$

• $i^{9}$

      $i^{9}=i^{4} .i^{4}.i$   $=(1)(1)i$

                           $=i$