Grade 12th passIntegral Calculus

hello,

how do i solve : (Z-2i)^4 = -8-8i sqrt3

thanks in advance

Evita Ammersingh

7 Years agoGrade 12th pass

7 Years ago

this ques is EXTREMELY easy.

all we need to do is to write RHS in re^itheta form and then apply de moivre rule.theorem.

note that -8-8i sqrt3= 16*e^(i4π/3)

also 16=2^4. let z= 2x

so we have (x – i)^4 = e^(i4π/3)

now x – i= [e^(i4π/3)]^1/4, which will have four distinct values due to moivres rule.

hence x= i + [e^(i4π/3)]^1/4

or z= 2i+2[e^(i4π/3)]^1/4

note that it is fairly elementary and easy to apply moivres theorem on [e^(i4π/3)]^1/4so you can do that on your own

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