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Find all sixth roots of the complex number 32√2(1 + i), and plot and label them on thecomplex plane by hand1

Question

Find all sixth roots of the complex number 32√2(1 + i), and plot and label them on thecomplex plane by hand1
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Solution 1

Step 1: Convert the complex number to polar form

The complex number 32√2(1 + i) can be written in polar form as r(cos θ + i sin θ), where r is the magnitude of the complex number and θ is the argument.

The magnitude r is given by √((Re(z))^2 + (Im(z))^2) = √((32√2)^2 + (32√2)^2) = 64.

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