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Consider the following expression: $$z = \sin \left ( y + it \right ) + \cos \left ( y - it \right )$$ where $\text{z, y}$ and $t$ are variables, and $i = \sqrt{-1}$ is a complex number. The partial differential equation derived from the above expression is

  1. $\frac{\partial ^{2}z}{\partial t^{2}} + \frac{\partial ^{2}z}{\partial y^{2}} = 0$
  2. $\frac{\partial ^{2}z}{\partial t^{2}} - \frac{\partial ^{2}z}{\partial y^{2}} = 0$
  3. $\frac{\partial z}{\partial t} - i \frac{\partial z}{\partial y} = 0$
  4. $\frac{\partial z}{\partial t} + i \frac{\partial z}{\partial y} = 0$
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