Question

The root of the equation z\4=_8

Answer 1

Step-by-step explanation:

We think you wrote:

z^4=-8

This deals with nonlinear equations.

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4 result(s) found

z=1.1892−1.1892i

z=−1.1892−1.1892i

z=−1.1892+1.1892i

z=1.1892+1.1892i

See steps

Step by Step Solution:

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Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

z^4-(-8)=0

Step by step solution :

STEP

1

:

Polynomial Roots Calculator :

1.1 Find roots (zeroes) of : F(z) = z4+8

Polynomial Roots Calculator is a set of methods aimed at finding values of z for which F(z)=0

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers z which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient

In this case, the Leading Coefficient is 1 and the Trailing Constant is 8.

The factor(s) are:

of the Leading Coefficient : 1

of the Trailing Constant : 1 ,2 ,4 ,8

Let us test ....

P Q P/Q F(P/Q) Divisor

-1 1 -1.00 9.00

-2 1 -2.00 24.00

-4 1 -4.00 264.00

-8 1 -8.00 4104.00

1 1 1.00 9.00

2 1 2.00 24.00

4 1 4.00 264.00

8 1 8.00 4104.00

Polynomial Roots Calculator found no rational roots

Equation at the end of step

1

:

z4 + 8 = 0

STEP

2

:

Solving a Single Variable Equation

2.1 Solve : z4+8 = 0

Subtract 8 from both sides of the equation :

z4 = -8

z = ∜ -8

The equation has no real solutions. It has 4 imaginary, or complex solutions.

z= 1.1892 + 1.1892 i

z= -1.1892 + 1.1892 i

z= -1.1892 - 1.1892 i

z= 1.1892 - 1.1892 i

Four solutions were found :

z= 1.1892 - 1.1892 i

z= -1.1892 - 1.1892 i

z= -1.1892 + 1.1892 i

z= 1.1892 + 1.1892 i