Question

If p =
$\sqrt{ - 1}$
Then find
$(1 - p) {}^{20}$
The best answer will be marked as brainliest.​

Answer 1

Answer:

-1024

Step-by-step explanation:

Given,

p = √(-1)

From theory of imaginary numbers,

√(-1) = i

So,

(1 - p)²⁰ = (1 - i)²⁰

Now,

(1 - i)²⁰ = {(1 - i)²}¹⁰......................................[By law of exponents]

= {1 - 2i + i² }¹⁰ ......................................[By expanding (1 - i)²]

= {- 2i }¹⁰ ......................................[By the definition i² = -1]

= {- 2}¹⁰ x {i}¹⁰ ......................................[By formula (ab)ⁿ = aⁿ x bⁿ]

= 1024 x {i}¹⁰  ......................................[2¹⁰ = 1024]

= 1024 x [{i}⁸]² ......................................[By law of exponents]

= 1024 x [i]²  ......................................[By the definition i⁸ = i]

= 1024 x -1  ......................................[By the definition i² = -1]

= -1024

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