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For z(1)=""^(6)sqrt((1-i)//(1+isqrt(3)))...

For `z_(1)=""^(6)sqrt((1-i)//(1+isqrt(3))),z_(2)=""^(6)sqrt((1-i)//(sqrt(3)+i))`, `z_(3)= ""^(6)sqrt((1+i) //(sqrt(3)-i))`, prove that `|z_(1)|=|z_(2)|=|z_(3)|`

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To prove that \( |z_1| = |z_2| = |z_3| \), we will calculate the modulus of each complex number step by step. ### Step 1: Calculate \( |z_1| \) Given: \[ z_1 = \sqrt[6]{\frac{1 - i}{1 + i\sqrt{3}}} \] ...
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