A complex number W multiplied by I can be regarded as a line segment connecting the point represented by W and the origin on the coordinate plane (in fact, there is a vector meaning in it, I wonder if you have learned it), and the length is unchanged by 90 clockwise.

Multiply the complex number w by the real number, such as √2. The graphic transformation on the coordinate plane is a line segment where the point indicated by W is connected with the origin, and the length becomes √2 times in the same direction. If it is negative, it is in the opposite direction.

In fact, it is better to understand its operation by converting complex numbers into exponential forms.

I hope I can help you.