Question Number 116051 by Hassen_Timol last updated on 30/Sep/20
$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{modulus}\:\mathrm{and}\:\mathrm{the}\:\mathrm{argument} \\ $$$$\mathrm{of}\:\:\:\mathrm{1}+{i}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right)\:\:? \\ $$
Answered by Dwaipayan Shikari last updated on 30/Sep/20
$$\mathrm{z}=\mathrm{1}+\mathrm{i}\left(\mathrm{1}+\sqrt{\mathrm{2}}\right) \\ $$$$\mid\mathrm{z}\mid=\sqrt{\mathrm{1}+\mathrm{1}+\mathrm{2}+\mathrm{2}\sqrt{\mathrm{2}}}=\sqrt{\mathrm{4}+\mathrm{2}\sqrt{\mathrm{2}}}\: \\ $$$$\mathrm{arg}\left(\mathrm{z}\right)=\mathrm{tan}^{−\mathrm{1}} \left(\sqrt{\mathrm{2}}+\mathrm{1}\right) \\ $$