# Determine if a Polynomial 2^26*(cos(-(52pi)/3)+isin(-(52pi)/3))

226⋅(cos(-52π3)+isin(-52π3))
A polynomial is a combination of terms separated using + or – signs. Polynomials cannot contain any of the following:
1. Variables raised to a negative or fractional exponent. (2x-2,x12,…).
2. Variables in the denominator. (1x,1×2,…).
3. Variables under a radical. (x,x3,…).
4. Special features. (trig functions, absolute values, logarithms, …).
Simplify the expression.
Raise 2 to the power of 26.
67108864⋅(cos(-52π3)+isin(-52π3))
Simplify each term.
Add full rotations of 2π until the angle is between 0 and 2π.
67108864⋅(cos(2π3)+isin(-52π3))
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second quadrant.
67108864⋅(-cos(π3)+isin(-52π3))
The exact value of cos(π3) is 12.
67108864⋅(-12+isin(-52π3))
Add full rotations of 2π until the angle is between 0 and 2π.
67108864⋅(-12+isin(2π3))
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
67108864⋅(-12+isin(π3))
The exact value of sin(π3) is 32.
67108864⋅(-12+i32)
Combine i and 32.
67108864⋅(-12+i32)
67108864⋅(-12+i32)
Simplify terms.
Apply the distributive property.
67108864(-12)+67108864i32
Cancel the common factor of 2.
Move the leading negative in -12 into the numerator.
67108864(-12)+67108864i32
Factor 2 out of 67108864.
2(33554432)-12+67108864i32
Cancel the common factor.
2⋅33554432-12+67108864i32
Rewrite the expression.
33554432⋅-1+67108864i32
33554432⋅-1+67108864i32
Multiply 33554432 by -1.
-33554432+67108864i32
Cancel the common factor of 2.
Factor 2 out of 67108864.
-33554432+2(33554432)i32
Cancel the common factor.
-33554432+2⋅33554432i32
Rewrite the expression.
-33554432+33554432(i3)
-33554432+33554432i3
-33554432+33554432i3
-33554432+33554432i3
Determine if the expression breaks any of the rules.
Does not break any of the rules
Determine if the expression is a polynomial.
Polynomial
Determine if a Polynomial 2^26*(cos(-(52pi)/3)+isin(-(52pi)/3))

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