Let z=reꜞᶿ=r(cosθ+isinθ).
z⁴=r⁴e⁴ꜞᶿ=r⁴(cos4θ+isin4θ)=3-4i.
r⁴cos4θ=3
r⁴sin4θ=-4
Dividing we get: tan4θ=-4/3 from which sin4θ=-4/5, cos4θ=3/5.
Squaring and adding: r⁸=25, r⁴=5, r=∜5=1.4953 approx.
4θ=-0.9273 approx, θ=-0.2318; sinθ=-0.2298, cosθ=0.9732.
z=1.4953(0.9732-0.2298i)=1.4552-0.3436i.