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1)
![|z|=\left|\left(\dfrac{1}{\sqrt{2}}-\dfrac{1}{\sqrt{2}}i\right)^3(3-4i)\right|\\ \\ \\
|z|=\left|\left(\dfrac{1}{\sqrt{2}}-\dfrac{1}{\sqrt{2}}i\right)^3\right|\left|(3-4i)\right|\\ \\ \\
|z|=\left|\left(\dfrac{1}{\sqrt{2}}-\dfrac{1}{\sqrt{2}}i\right)\right|^3\left|(3-4i)\right|\\ \\ \\
|z|=\sqrt{\left( \dfrac{1}{\sqrt{2}}\right)^2+\left( \dfrac{1}{\sqrt{2}}\right)^2}^3\times \sqrt{3^2+4^2}\\ \\ \\
|z|=5 |z|=\left|\left(\dfrac{1}{\sqrt{2}}-\dfrac{1}{\sqrt{2}}i\right)^3(3-4i)\right|\\ \\ \\
|z|=\left|\left(\dfrac{1}{\sqrt{2}}-\dfrac{1}{\sqrt{2}}i\right)^3\right|\left|(3-4i)\right|\\ \\ \\
|z|=\left|\left(\dfrac{1}{\sqrt{2}}-\dfrac{1}{\sqrt{2}}i\right)\right|^3\left|(3-4i)\right|\\ \\ \\
|z|=\sqrt{\left( \dfrac{1}{\sqrt{2}}\right)^2+\left( \dfrac{1}{\sqrt{2}}\right)^2}^3\times \sqrt{3^2+4^2}\\ \\ \\
|z|=5](https://tex.z-dn.net/?f=%7Cz%7C%3D%5Cleft%7C%5Cleft%28%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D-%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7Di%5Cright%29%5E3%283-4i%29%5Cright%7C%5C%5C+%5C%5C+%5C%5C%0A%7Cz%7C%3D%5Cleft%7C%5Cleft%28%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D-%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7Di%5Cright%29%5E3%5Cright%7C%5Cleft%7C%283-4i%29%5Cright%7C%5C%5C+%5C%5C+%5C%5C%0A%7Cz%7C%3D%5Cleft%7C%5Cleft%28%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D-%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7Di%5Cright%29%5Cright%7C%5E3%5Cleft%7C%283-4i%29%5Cright%7C%5C%5C+%5C%5C+%5C%5C%0A%7Cz%7C%3D%5Csqrt%7B%5Cleft%28+%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5Cright%29%5E2%2B%5Cleft%28+%5Cdfrac%7B1%7D%7B%5Csqrt%7B2%7D%7D%5Cright%29%5E2%7D%5E3%5Ctimes+%5Csqrt%7B3%5E2%2B4%5E2%7D%5C%5C+%5C%5C+%5C%5C%0A%7Cz%7C%3D5)
2)
![|w|=\left|\dfrac{\sqrt{\sqrt{15}+i}~(3+5i)}{\sqrt{34}i}\right|\\ \\ \\
|w|=\dfrac{\left|\sqrt{\sqrt{15}+i}\right|~\left|(3+5i)\right|}{\left|\sqrt{34}i\right|}\\ \\ \\
|w|=\dfrac{\left|\sqrt{\sqrt{15}+i}\right|~\sqrt{34}}{\sqrt{34}}\\ \\ \\
|w|=\left|\sqrt{\sqrt{15}+i}\right|\\ \\ \\
|w|=\sqrt{\left|\sqrt{15}+i\right|}\\ \\ \\
|w|=4 |w|=\left|\dfrac{\sqrt{\sqrt{15}+i}~(3+5i)}{\sqrt{34}i}\right|\\ \\ \\
|w|=\dfrac{\left|\sqrt{\sqrt{15}+i}\right|~\left|(3+5i)\right|}{\left|\sqrt{34}i\right|}\\ \\ \\
|w|=\dfrac{\left|\sqrt{\sqrt{15}+i}\right|~\sqrt{34}}{\sqrt{34}}\\ \\ \\
|w|=\left|\sqrt{\sqrt{15}+i}\right|\\ \\ \\
|w|=\sqrt{\left|\sqrt{15}+i\right|}\\ \\ \\
|w|=4](https://tex.z-dn.net/?f=%7Cw%7C%3D%5Cleft%7C%5Cdfrac%7B%5Csqrt%7B%5Csqrt%7B15%7D%2Bi%7D%7E%283%2B5i%29%7D%7B%5Csqrt%7B34%7Di%7D%5Cright%7C%5C%5C+%5C%5C+%5C%5C%0A%7Cw%7C%3D%5Cdfrac%7B%5Cleft%7C%5Csqrt%7B%5Csqrt%7B15%7D%2Bi%7D%5Cright%7C%7E%5Cleft%7C%283%2B5i%29%5Cright%7C%7D%7B%5Cleft%7C%5Csqrt%7B34%7Di%5Cright%7C%7D%5C%5C+%5C%5C+%5C%5C%0A%7Cw%7C%3D%5Cdfrac%7B%5Cleft%7C%5Csqrt%7B%5Csqrt%7B15%7D%2Bi%7D%5Cright%7C%7E%5Csqrt%7B34%7D%7D%7B%5Csqrt%7B34%7D%7D%5C%5C+%5C%5C+%5C%5C%0A%7Cw%7C%3D%5Cleft%7C%5Csqrt%7B%5Csqrt%7B15%7D%2Bi%7D%5Cright%7C%5C%5C+%5C%5C+%5C%5C%0A%7Cw%7C%3D%5Csqrt%7B%5Cleft%7C%5Csqrt%7B15%7D%2Bi%5Cright%7C%7D%5C%5C+%5C%5C+%5C%5C%0A%7Cw%7C%3D4)
2)
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