Solution
= Solution
Using <Euler's formula>, the <complex exponential function> satisfies
$$
e^{x+iy}=e^x(\cos y+i\sin y).
$$
Hence
$$
\boxed{\operatorname{Re}(e^z)=e^x\cos y,
\qquad \operatorname{Im}(e^z)=e^x\sin y}.
$$
= Solution
Using <Euler's formula>, the <complex exponential function> satisfies
$$
e^{x+iy}=e^x(\cos y+i\sin y).
$$
Hence
$$
\boxed{\operatorname{Re}(e^z)=e^x\cos y,
\qquad \operatorname{Im}(e^z)=e^x\sin y}.
$$