Answer:
Z0 = 7 ( cos 60° + isin60°)
Z1 = 7( cos180° + isin180° )
Z2 = 7 ( cos300° + isin300°)
Step-by-step explanation:
Given that;
cube root of -343
so, z = -343 + 0i
∴ r = √ (( -343)² + (0)²) = 343
so tan∅ = y/x ⇒ tan∅ = 0/-343
∅ = tan⁻¹ (0/-343)
= 0 or 180°
but we are going yo make use of 180° since -343 is negative x-axis
Zk = ∛343 ( cos 180/3 + 360K/3) + isin(180/3 + 360k/3)
here k = 0, 1, 2, 3 .........
SO z0 = z1 = z2 = ???
k=0
Z0 = ∛343 ( cos 180/3 + isin180/3)
= ∛343 ( cos 60° + isin60°)
Z0 = 7 ( cos 60° + isin60°)
K=1
Z1 = ∛343 ( cos 180/3 + 360×1 / 3 + isin180/3 + 360×1 / 3 )
= ∛343 ( cos180° + isin180°)
Z1 = 7( cos180° + isin180° )
K=2
Z2 = ∛343 ( cos 180/3 + 360×2 / 3 + isin180/3 + 360×2 / 3 )
= ∛343 ( cos300° + isiN300°)
Z2 = 7 ( cos300° + isin300°)
