16i

16i is a complex number obtained by multiplying the imaginary unit i by 16. It equals 0 + 16i, so its real part is 0 and its imaginary part is 16. In the complex plane, it lies on the positive imaginary axis at the point (0, 16). The modulus of 16i is 16, and its argument is π/2. It can be written in polar form as 16 e^{iπ/2}, or equivalently 16(cos π/2 + i sin π/2).

The powers of 16i follow the standard rule for powers of i: (16i)^n = 16^n i^n. For example, (16i)^2 = -256, (16i)^3 = -4096 i, and (16i)^4 = 65536. Thus even powers are real and negative (for n > 0), while odd powers are imaginary. Because i^n cycles with period 4, the sequence of powers of 16i exhibits a repeating pattern of real and imaginary values.

The complex conjugate of 16i is -16i, and its magnitude remains 16 under conjugation. As a scaled imaginary unit, 16i represents a purely imaginary quantity and is commonly used in algebra and engineering contexts to denote imaginary-valued quantities or to describe rotations in the complex plane, since multiplying by i corresponds to a 90-degree rotation.