Solution
= Solution
In <polar form of a complex number>, $1+i=\sqrt2\,e^{i\pi/4}$. By <De Moivre's theorem>,
$$
(1+i)^{10}=2^5e^{5\pi i/2}=32i,
\qquad\boxed{\Re z=0,\qquad\Im z=32.}
$$
= Solution
In <polar form of a complex number>, $1+i=\sqrt2\,e^{i\pi/4}$. By <De Moivre's theorem>,
$$
(1+i)^{10}=2^5e^{5\pi i/2}=32i,
\qquad\boxed{\Re z=0,\qquad\Im z=32.}
$$