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The set of complex number z with | z | = 1 under the operation * denote by z1 * z2 = | z1 | ·z2
- a)group but not abelian
- b)group but not cyclic
- c)cyclic group
- d)None of the above
Correct answer is option 'D'. Can you explain this answer?
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The set of complex number z with| z| = 1 under theoperation *denotebyz...
The operation * on the set of complex numbers z with |z| = 1 is defined as follows:
For any two complex numbers z1 and z2 with |z1| = |z2| = 1, their operation * is given by:
z1 * z2 = |z1|
In other words, when two complex numbers z1 and z2 with magnitude 1 are multiplied under this operation *, the result is the magnitude of z1.
Note that the operation * does not depend on the actual values of z1 and z2, only on their magnitudes being 1.
For any two complex numbers z1 and z2 with |z1| = |z2| = 1, their operation * is given by:
z1 * z2 = |z1|
In other words, when two complex numbers z1 and z2 with magnitude 1 are multiplied under this operation *, the result is the magnitude of z1.
Note that the operation * does not depend on the actual values of z1 and z2, only on their magnitudes being 1.
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