Asked by Seble wongel
Let Z be a complex number.whicj of the following is solution set of z^3-iz=0
Answers
Answered by
Anonymous
If you tried to copy and paste the answer choices, that does not work on this site.
Answered by
mathhelper
Don't see any "following", but expect to see something like ....
z^3-iz=0
z(z^2 - i) = 0
z = 0 or z = ±√ i
Now about that √ i
let a + bi = √ i
a^2 + 2abi + b^2 i^2 = i
a^2 - b^2 + 2abi = 0 + i
a^2 - b^2 = 0
a = ±b
and
2abi = i
2ab = 1
2a^2 = 1
a = ±1/√2 = ±√2 / 2
z=0 , z = ±√2 / 2 ± (√2 / 2) i = ±(√2/2)(1 + i)
z^3-iz=0
z(z^2 - i) = 0
z = 0 or z = ±√ i
Now about that √ i
let a + bi = √ i
a^2 + 2abi + b^2 i^2 = i
a^2 - b^2 + 2abi = 0 + i
a^2 - b^2 = 0
a = ±b
and
2abi = i
2ab = 1
2a^2 = 1
a = ±1/√2 = ±√2 / 2
z=0 , z = ±√2 / 2 ± (√2 / 2) i = ±(√2/2)(1 + i)