14i

14i denotes a complex number in standard form a + bi, where a = 0 and b = 14. It is 14 times the imaginary unit i, with the defining property i^2 = -1. Therefore, 14i is a purely imaginary number, located on the imaginary axis of the complex plane at the point (0, 14).

Basic properties include a modulus of 14, since the magnitude is sqrt(0^2 + 14^2) = 14, and an argument of π/2 (90 degrees). In polar form, 14i can be written as 14 e^{iπ/2} or 14 cis(π/2).

Algebraic operations with 14i follow standard complex arithmetic. Adding 14i to a complex number a + bi yields a + (b + 14)i. Multiplying 14i by i gives -14, since i^2 = -1. The reciprocal is 1/(14i) = -i/14, and the complex conjugate is -14i.

In context, 14i serves as a basis vector along the imaginary axis. It is used in complex arithmetic and phasor representations in various fields of mathematics and engineering. In electrical engineering contexts, the symbol j is often used instead of i to denote the imaginary unit, so 14i and 14j describe the same mathematical quantity. The real part of 14i is zero, underscoring its purely imaginary nature.