\(z =(−1 + i )^(1/3)\)
\(r=\sqrt((-1)^2+1^2)\)
\(r=\sqrt(1+1^2)\)
\(r=\sqrt(1+1)\)
\(r=\sqrt(2)\)
\(tan(\Theta)=1/-1\)
\(tan(\Theta)=-1\)
\(\Theta=tan^-1(-1)\)
\(\Theta=-\pi/4\)
\(\sqrt(2)e^(-\pi/4i)^(1/3)\)
\(\sqrt(2)^(1/3)e^(-\pi/12i)\)
\(\sqrt(2)^(1/3)*(cos(-\pi/12)+isin(-\pi/12))\)
\(\sqrt(2)^(1/3)*(0.965925826289 +isin(-\pi/12))\)
\(\sqrt(2)^(1/3)*(0.965925826289 +i*-0.258819045103)\)
\(\ 1.414213562373095)^(1/3)*(0.965925826289 +i*-0.258819045103)\)
\(\ 1.122462048309373*(0.965925826289 +i*-0.258819045103)\)
\(\ 1.084215081491274550528506797 +i*-0.290514555507789375384650419\)
\(\ 1.084215081491274550528506797 + -0.290514555507789375384650419i\)
Answer 1:\(\ 1.084215081491274550528506797 -0.290514555507789375384650419i\)
\(\sqrt(2)e^(7\pi/4i)^(1/3)\)
\(\sqrt(2)^(1/3)e^(7\pi/12i)\)
\(\sqrt(2)^(1/3)*(cos(7\pi/12)+isin(7\pi/12))\)
\(\sqrt(2)^(1/3)*(-0.258819045103 +isin(7\pi/12))\)
\(\sqrt(2)^(1/3)*(-0.258819045103 +i* 0.965925826289)\)
\(\ 1.414213562373095)^(1/3)*(-0.258819045103 +i* 0.965925826289)\)
\(\ 1.122462048309373*(-0.258819045103 +i* 0.965925826289)\)
\(\ -0.290514555507789375384650419 +i* 1.084215081491274550528506797\)
Answer 2:\(\ -0.290514555507789375384650419 +1.084215081491274550528506797i\)
\(\sqrt(2)e^(15\pi/4i)^(1/3)\)
\(\sqrt(2)^(1/3)e^(15\pi/12i)\)
\(\sqrt(2)^(1/3)*(cos(15\pi/12)+isin(15\pi/12))\)
\(\sqrt(2)^(1/3)*(-0.707106781187 +isin(15\pi/12))\)
\(\sqrt(2)^(1/3)*(-0.707106781187 +i* -0.707106781187)\)
\(\ 1.414213562373095)^(1/3)*(-0.707106781187 +i* -0.707106781187)\)
\(\ 1.122462048309373*(-0.793700525984607637192165751 +i* -0.793700525984607637192165751)\)
\(\ -0.793700525984607637192165751 +i*-0.793700525984607637192165751\)
\(\ -0.793700525984607637192165751 +-0.793700525984607637192165751i\)
Answer 3:\(\ -0.793700525984607637192165751 -0.793700525984607637192165751i\)
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