If z is a non-real complex number, then the minimum value of \frac{Im \: z^{5}}{\left ( Im\: z \right )^{5}}

Answers (1)

Let z = x+ iy

\frac{Im \: z^{5}}{\left ( Im\: z \right )^{5}}

\\ = \frac{Im(x+iy)^5}{y^5} \\ = \frac{1}{y^5}[\cancel{^5C_0x^5 }+^5C_1x^4(iy)+\cancel{^5C_2x^3(iy)^2}+^5C_3x^2(iy)^3+\cancel{^5C_4x(iy)^4}+^5C_5(iy)^5 ]

 

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