Question

Prove that (- 1 + i)^7 = -8(1 + i)​

Answer 1

Answer:

-1+I squre 7is equal 8 1+7is equal 8

Answer 2

By the given explanation, it is proven that (-1 + i)⁷ = -8(1 + i)​.

Given:

Prove that (-1 + i)² = -8(1 + i)​  

Solution:

The given statement is (-1 + i)⁷ = -8(1 + i)​  

Take LHS (-1 + i)⁷ it can be simplified as follows

=> (-1 + i)⁷ = (-1 + i)²(-1 + i)²(-1 + i)² (- 1 + i)  

Using Algebraic identity (a + b)² = a² + b² + 2ab  

=>  (-1 + i)² = (-1)² + 2(-1)(i) + (i)²

= 1 - 2i - 1 = -2i

=> (-1 + i)²  = -2i

=>  (-1 + i)²(-1 + i)²(-1 + i)² (- 1 + i)    

= (-2i) (-2i) (-2i) (-1 + i)

= - 8 (i)³(-1 + i)

= - 8(-1)(i) (-1 + i)

=  8 (- i + (i)²)

=  8 (- i - 1)

= - 8 (1 + i)  

Hence, (-1 + i)⁷ = -8(1 + i)​    

Therefore,

By the given explanation, it is proven that (-1 + i)⁷ = -8(1 + i)​.  

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