A $90^\circ$ rotation around the origin in the counter-clockwise direction is applied to $7 + 2i.$  What is the resulting complex number?
To rotate a complex number $a + bi$ around the origin by $90^\circ$ counter-clockwise, we can multiply it by $i$, which is equivalent to rotating by $90^\circ$ in the complex plane. So, we have $(7 + 2i) \cdot i = 7i - 2 + 0i$. This simplifies to $-2 + 7i$, which is the resulting complex number. 