Question

Find the value of w80​

Answer 1

Answer:

what W stands for?

Step-by-step explanation:

what W stands for?

Answer 2

$\bf {w}^{80} = {w}^{2}$

or

$\bf {w}^{80} = - (1 + w)$

Given:

• ${w}^{80}$

To find:

• Find the value of expression.

Solution:

Concept/Formula to be used:

We know that ,

$1, \: w ,\: and \: {w}^{2}$ are complex cube roots of unity.

Properties of these roots are

1. $\bf 1 + w + {w}^{2} = 0$
2. $\bf {w}^{3} = 1$

Step 1:

Simplify power of w.

Write the power of 'w' in multiple of 3.

$80 = 78 + 2$

$80 = (26 \times 3) + 2$

$\bf {w}^{80} = {w}^{(26 \times 3) + 2}$

Step 2:

Simplify the expression.

We know that

$\bf {x}^{a + b} = {x}^{a} {x}^{b}$

and

$\bf {x}^{ab} = {( {x}^{a} )}^{b}$

So,

${w}^{26 \times 3 + 2} = {( {w}^{3} })^{26} {w}^{2}$

or

${w}^{80} = {(1)}^{26} {w}^{2}$

$\bf {w}^{80} = {w}^{2}$

or

$\bf {w}^{80} = - (1 + w)$

Thus,

$\bf {w}^{80} = {w}^{2}$ or $\bf {w}^{80} = - (1 + w)$

Learn more:

1) If w denotes the complex cube-root of unity, prove the following

i) (w² + w - 1)³ = -8

ii) (a + b) + (aw + bw²) + (aw²...

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2) Find the value of

i) w¹⁸

ii) w²¹

iii) w⁻³⁰

iv) w⁻¹⁰⁵

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