Phy 419 Find the velocity of the particle positive charge

Find the velocity of the particle, v(𝑑), if its initial velocity is v0 = (π‘₯τ°0,𝑦τ°0,𝑧τ°0).
Hint: Introduce the compex number πœ‚ = π‘₯ 𝑖𝑦 and solve for πœ‚τ°, then find the velocity components as
π‘₯τ° = Re(πœ‚τ°) and 𝑦τ° = Im(πœ‚τ°) (you don’t have to solve for π‘₯(𝑑), 𝑦(𝑑), and 𝑧(𝑑), only for π‘₯τ°(𝑑), 𝑦τ°(𝑑), 𝑧τ°(𝑑)). Partial answer: 𝑦τ°(𝑑) = π‘žπΈ (cos(πœ”π‘‘) βˆ’ 1) 𝑦τ°0 cos(πœ”π‘‘) βˆ’ π‘₯τ°0 sin(πœ”π‘‘) .