CVEL4

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Find where \sin z=\cos z\,.

{\frac  {e^{{iz}}-e^{{-iz}}}{2i}}={\frac  {e^{{iz}}+e^{{-iz}}}{2}}\,

e^{{iz}}(1-i)=e^{{-iz}}(1+i)\,

e^{{2iz}}={\frac  {1+i}{1-i}}\cdot {\frac  {1+i}{1+i}}={\frac  {(1+i)^{2}}{2}}=i=e^{{i{\frac  {\pi }{2}}}}\,

Therefore

2z={\frac  {\pi }{2}}+k2\pi ,k\in {\mathbb  {Z}}\,

z={\frac  {\pi }{4}}+k\pi ,k\in {\mathbb  {Z}}\,


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