Question

if 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is _.

Answer 1

Answer: If 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate 7-i5.

Step-by-step explanation:

• We know that when a complex number $z=a+ib$ is a root of a polynomial with degree 'n' , then the conjugate of the complex number ($\overline{z}=a-ib$) is also a root of the same polynomial.

Given: 7+5i is a zero of a polynomial function of degree 5 with coefficients

Here, 7+5i is a complex number.

So, it conjugate ($\overline{7+5i}=7-5i$) is also a zero of a polynomial function.

Hence, if 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate 7-i5.

Answer 2

If 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate which is 7 - 5i

The standard form of writing complex numbers with real and imaginary values is expressed as:

z = x + iy

The conjugate of the complex number will be y = x - iy

• A complex number and its conjugate both have the same degree with coefficient.

Given the polynomial 7 + 5i. If 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate which is 7 - 5i

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