Are operations with complex numbers similar to operations with polynomials?

When a negative number is expressed inside the square root operation, the imaginary unit ${\displaystyle i=\sqrt{-1}}$ is defined to represent the number. The number containing an imaginary unit is known as a complex number.
A polynomial is an expression that contains terms in one or more variables that have exponents to them. These terms are either added, multiplied, or subtracted to obtain the complete expression of the polynomial.
The addition of polynomials with a single variable can be done by adding the terms with the same exponents of the variable. Addition in complex numbers is similar to polynomial when the imaginary unit i is considered to be variable with exponent 1 and the real parts of the complex number is considered to be multiplied with the imaginary unit having exponent 0. Thus the corresponding imaginary and real parts of the complex numbers are added.
The addition of polynomials with a single variable can be done by adding the terms with the same exponents of the variable. Addition in complex numbers is similar to polynomial when the imaginary unit i is considered to be variable with exponent 1 and the real parts of the complex number is considered to be multiplied with the imaginary unit having exponent 0. Thus the corresponding imaginary and real parts of the complex numbers are added.${\displaystyle i^2=-1}$ to simplify the product.
The subtraction of polynomials is carried out as the addition of one polynomial with the negative of another polynomial. Similarly, the addition of complex numbers is the addition of one complex number with the negative of another complex number.
Division operation in polynomials is not the same as division operation in complex numbers. Division in polynomials is carried out similarly to the division in real numbers. Division in complex numbers is obtained when the represented fraction of division is rationalized by multiplying the numerator and the denominator with the conjugate of the complex number in the denomiantor.