Knowee
Questions
Features
Study Tools

If z5 = (z – 1)5, then the roots are represented in the argand plane by the points that are

Question

If z5 = (z – 1)5, then the roots are represented in the argand plane by the points that are

🧐 Not the exact question you are looking for?Go ask a question

Solution

To solve the equation z5 = (z – 1)5, we can start by expanding both sides using the binomial theorem.

On the left side, we have z5 = z * z * z * z * z.

On the right side, we have (z – 1)5 = (z – 1) * (z – 1) * (z – 1) * (z – 1) * (z – 1).

Expanding both sides further, we get:

z5 = z * z * z * z * z (z – 1)5 = (z – 1) * (z – 1) * (z – 1) * (z – 1) * (z – 1)

Now, we can equate the corresponding terms on both sides:

z = z – 1 z = z – 1 z = z – 1 z = z – 1 z = z – 1

Simplifying each equation, we find that z = 1.

Therefore, the equation z5 = (z – 1)5 has only one root, which is z = 1.

In the Argand plane, this root is represented by the point (1, 0), which lies on the real axis.

This problem has been solved

Similar Questions

z 2 −5z−5=3z

What value of z is a solution to this equation?5z=z+4

Solve the equation.*1 pointz=1/2 or -5/2z=1/3 or 5/2z=5/3 or -1/2z=-5/3 or 1/2The values of x in the equation below are __________.*1 pointX=0 or 3/5X=0 or 5X=3 or 5X=0 or 3Which of the following pairs are the values of x in the equation below?*1 point3/2, 9-3, 9/2-2/3, 9-5 or -2Solve the equation below. *1 point5 or -25 or 2-5 or 2-5 or -2Solving the equation below, a = ?*1 point-3, 1-1, 3-1, -33, 1

Which of the following polynomial functions have exactly 5 roots, including all real and imaginary roots?Responsesf(x)=5x4+x3−x2+x−5𝑓(𝑥)=5𝑥4+𝑥3−𝑥2+𝑥−5f of x is equal to 5 x to the 4th power plus x cubed minus x squared plus x minus 5f(x)=4x5+3x4+2x3+x2+x𝑓(𝑥)=4𝑥5+3𝑥4+2𝑥3+𝑥2+𝑥f of x is equal to 4 x to the 5th power plus 3 x to the 4th power plus 2 x raised to the 3 power plus x squared plus xf(x)=5x6−5x4+5x2−5𝑓(𝑥)=5𝑥6−5𝑥4+5𝑥2−5f of x is equal to 5 x to the 6th power minus 5 x to the 4th power plus 5 x squared minus 5f(x)=4x4−3x3+2x2−1

Which of the following polynomial functions have exactly 5 roots, including all real and imaginary roots?Responsesf(x)=5x4+x3−x2+x−5𝑓(𝑥)=5𝑥4+𝑥3−𝑥2+𝑥−5f of x is equal to 5 x to the 4th power plus x cubed minus x squared plus x minus 5f(x)=4x5+3x4+2x3+x2+x𝑓(𝑥)=4𝑥5+3𝑥4+2𝑥3+𝑥2+𝑥f of x is equal to 4 x to the 5th power plus 3 x to the 4th power plus 2 x raised to the 3 power plus x squared plus xf(x)=5x6−5x4+5x2−5𝑓(𝑥)=5𝑥6−5𝑥4+5𝑥2−5f of x is equal to 5 x to the 6th power minus 5 x to the 4th power plus 5 x squared minus 5f(x)=4x4−3x3+2x2−1𝑓(𝑥)=4𝑥4−3𝑥3+2𝑥2−1f of x is equal to 4 x to the 4th power minus 3 x cubed plus 2 x squared minus 1Graphing Calculator

1/1

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.