100 POINTS AND BRAINLIEST FOR THIS WHOLE SEGMENT a) Find zw, Write your answer in both polar form with ∈ [0, 2pi] and in complex form.

b) Find z^10. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.

c) Find z/w. Write your answer in both polar form with ∈ [0, 2pi] and in complex form.

d) Find the three cube roots of z in complex form. Give answers correct to 4 decimal

places.

z1×z2=−5√3−5i

Step-by-step explanation:

If we have two complex numbers z 1 = r 1 ( cos α + i sin α ) and z 2 = r 2 ( cos β + i sin β )

z1×z2=r1r2(cosαcosβ+icosαsinβ+isinαcosβ+i2sinαsinβ)orz1×z2=r1r2((cosαcosβ−sinαsinβ)+i(cosαsinβ+sinαcosβ)

or z 1 × z 2 = r 1 r 2 ( cos ( α + β ) + i sin ( α + β ) ) Here we have z 1 = 2 ( cos ( 5 π 6 ) + i sin ( 5 π 6 ) ) and z 2 = 5 ( cos ( π 3 ) + i sin ( π 3 ) and z 1 × z 2 = 2 × 5 ( cos ( 5 π 6 + π 3 ) + i sin ( 5 π 6 + π 3 ) ) = 10 ( cos ( 7 π 6 ) + i sin ( 7 π 6 ) ) = 10 ( cos ( π + π 6 ) + i sin ( π + π 6 ) ) = 10 ( − cos ( π 6 ) − i sin ( π 6 ) ) = − 10 ( √ 3 2 + i 2 ) = − 5 √ 3 − 5 i

P.S My caculations might be off, so  i hope it helps at least.

middle maybe?

step-by-step explanation: