Question

please also give explanations
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Answer 1

$(1 - \sqrt{ - 1) ^{20} }$

1-p

answee will be 1 - p maybe i m not sure because i didnt understood it perfectly

Answer 2

Answer:

Step-by-step explanation:

(1-i)^20             p = √-1

1-i = √2((cos135) - isin(135))

tanβ = b/a = -1/1 , therefore, β = 135

a=1, b=-1

we know de-moivre's theorem

(a - ib)^n = (r(cosβ - isinβ))^n = r^n(cosnβ - isinnβ )

where, r = √(a² + b²)

here, a = 1, b = -1

r = √2

(1 - i)^20 = (√2)^20 (cos-20π/4 - isin-20π/4)

               = 2^10 (cos-5π - isin-5π)

               = 1024(-1 - 0)

               = -1024