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Complex Number Argument Calculation

Very Hard Additional Math Topics Complex Numbers

Consider the complex number z defined as:

z=3+4i

where i is the imaginary unit. Calculate the modulus and argument of the complex number w given by:

w=z2+4z+8

Next, express w in the form of a + bi, where a and b are real numbers. Finally, find the value of the argument of w rounded to three decimal places.

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