Consider the following. Cube roots of −343 (a) Use the formula zk = n r cos θ + 2πk n + i sin θ + 2πk n to find the indicated roots of the complex number. (Enter your answers in trigonometric form. Let 0 ≤ θ < 2π.) z0 = z1 = z2 =

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°)

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq

answer: ur v dumb

step-by-step explanation: