If z is a complex function and z^{3}=8i, what are

Pam Stokes 2022-01-18 Answered
If z is a complex function and z3=8i, what are all the values of z?
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Vivian Soares
Answered 2022-01-19 Author has 36 answers
z3=8i
z38i=0
z3+(2i)3=0
(z+2i)(z2+(2i)22iz)=0
(z+2i)(z22iz4)=0
z=2i
or z22iz4=0
z=2i±4+162
z=i±3
So roots are 2i,i+3,i3
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aquariump9
Answered 2022-01-20 Author has 40 answers
z3=8i=8ei(π2+2nπ)
where nZ
z=2ei(π6+2nπ3)
z=2eiπ6,2ei(5π6),2ei(3π2)
z=3+i,3+i,2i
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alenahelenash
Answered 2022-01-24 Author has 343 answers
Let ω=e2iπ3=12+i32 is a root of unit. So the roots of Z3=1 are:ω0=1;ω and ω2=ω We have: z3=8iz3=(2i)3(z2i)3=1 So: z2i=ωkk0;1;2. Thus The root of the equation z3=8i are: z=2iω˙kk0;1;2 i.e. z=2i or z=3+i or z=3+i
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