10.21 Write the complex number $z=\sin 36^{\circ}+i \cos 54^{\circ}$ in trigonometric form.
10.21 Since $\cos 54^{\circ}=\sin 36^{\circ}$, then

$$
z=\sin 36^{\circ}+i \cos 54^{\circ}=\sin 36^{\circ}+i \sin 36^{\circ}=\sin 36^{\circ}(1+i)
$$

But $1+i=\sqrt{2}\left(\cos 45^{\circ}+i \sin 45^{\circ}\right)$ and, therefore, the trigonometric form of this number is

$$
z=\sqrt{2} \sin 36^{\circ}\left(\cos 45^{\circ}+i \sin 45^{\circ}\right)
$$