Calculating the Imaginary Part of (1-2i)^2-i

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To find the imaginary part of (1-2i)^2 - i, first calculate (1-2i)^2, resulting in 1 - 4i + 4, which simplifies to 5 - 4i. Next, express 1-2i in polar form to facilitate the calculation of (1-2i)^-i. The polar form is derived from the modulus and argument of the complex number. After obtaining the polar form, apply the exponent to find the final result and extract the imaginary part. The process involves both algebraic manipulation and understanding of complex numbers in polar coordinates.
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How can i find The imaginary part of (1-2i)^2-i.

This is what i have done so far:
(1-2i)^2 (1-2i)^-i

=(1-4i+4)(1-2i)^-i
 
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Use the polar form of 1-2i.
 

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