if z = 3 - 4i, then z4 - z3 + 3z2 + 99z -95 is equal to plz give - Maths - Complex Numbers and Quadratic Equations

Question

if z = 3 - 4i, then z4 - z3 + 3z2
+ 99z -95 is equal to
plz give me the shortest way if any

Ashwini Kumar · Accepted Answer

We have,z=3-4i⇒z2=3-4i2⇒z2=32+4i2-2×3×4i⇒z2=9-16-24i⇒z2=-7-24iNow,z4-z3+3z2+99z-95=z4+3z2-z3+99z-95=z2z2+3-zz2-99-95=-7-24i-7-24i+3-3-4i-7-24i-99-95=-7-24i-4-24i-3-4i-106-24i-95=7+24i4+24i+3-4i106+24i-95=28+168i+96i+576i2+318+72i-424i-96i2-95=28+168i+96i-576+318+72i-424i+96-95=28-576+318+96-95+168i+96i+72i-424i=-229-88i

if z = 3 - 4i, then z4 - z3 + 3z2 + 99z -95 is equal to plz give me the shortest way if any

if z = 3 - 4i, then z⁴ - z³+ 3z² + 99z -95 is equal to
plz give me the shortest way if any