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A simple exercise requiring the calculation of the modulus and argument of complex numbers.

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Below you will be asked to find the modulus and argument of two different complex numbers. Give your answers to 2 decimal places, with the arguments in the interval $[0,2\\pi)$.

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The modulus of a complex number $a + ib$ is calculated as $r = \\sqrt{a^2 + b^2}$. So for $z = \\var{real_z} + \\var{imag_z}i$ the value of the modulus is $|z| = \\sqrt{\\var{real_z}^2 + \\var{imag_z}^2} =\\var{mod_z}$.

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What is the value of the modulus of $z = \\simplify{{real_z} + {imag_z} i}$?

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What is the value of the argument of $z = \\simplify{{real_z} + {imag_z} i}$?

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What is the value of the modulus of $w = \\simplify{{real_w} + {imag_w} i}$?

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What is the value of the argument of $w = \\simplify{{real_w} + {imag_w} i}$?

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