Determine with explanation the dimension of (a) complex as a vector space over complex (b) complex as a vector space over reals (c) complex ^3 as a vector over complex (d) complex ^3 as a vector space over reals. I am thinking the following:
(a) dim=1:Complex numbers are in the form of a+bi so hence dimension = 1?
(b) dim =2: There are two part hence dimension is 2.
(c) dim = 3: Complex numbers are in the form of a+bi so 3x1 =3
(d) dim = 6: There are two part in real so 3x2 = 6.
However, I am unsure if this is correct. Can you please define dimension as well as an explanation why or why not I may be correct. If correct is my explanation appropriate or what is missing.
Determine with explanation the dimension of (a) complex as a vector space over complex (b) complex...
Find all solutions to the equation x' +27 = 0 over the Complex Numbers. Do all parts (a)-(d): (a) Graph complex number -27+0.i as a vector in trigonometric form (b) Use De Moivre's Theorem to find one cube root of -27 (c) Graph all three solutions as vectors (in trigonometric form) on the xy-plane (d) Lastly, convert each solution from trigonometric form reise to standard form a +bi
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