Solve v^43-i^6 - ScanMath

Question

Simplify the expression

3 v^{4} + 1

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Find the roots

v_{1} = - \frac{4 108}{6} + \frac{4 108}{6} i, v_{2} = \frac{4 108}{6} - \frac{4 108}{6} i

Alternative Form

v_{1} \approx - 0.537285 + 0.537285 i, v_{2} \approx 0.537285 - 0.537285 i

Evaluate

v^{4} \times 3 - i^{6}

To find the roots of the expression,set the expression equal to 0

v^{4} \times 3 - i^{6} = 0

Evaluate the power

More Steps

v^{4} \times 3 - (- 1) = 0

Use the commutative property to reorder the terms

3 v^{4} - (- 1) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

3 v^{4} + 1 = 0

Move the constant to the right-hand side and change its sign

3 v^{4} = 0 - 1

Removing 0 doesn't change the value,so remove it from the expression

3 v^{4} = - 1

Divide both sides

\frac{3 v ^{4}}{3} = \frac{- 1}{3}

Divide the numbers

v^{4} = \frac{- 1}{3}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

v^{4} = - \frac{1}{3}

Take the root of both sides of the equation and remember to use both positive and negative roots

v = \pm 4 - \frac{1}{3}

Simplify the expression

More Steps

v = \pm (\frac{4 108}{6} - \frac{4 108}{6} i)

Separate the equation into 2 possible cases

v = \frac{4 108}{6} - \frac{4 108}{6} i v = - \frac{4 108}{6} + \frac{4 108}{6} i

Solution

v_{1} = - \frac{4 108}{6} + \frac{4 108}{6} i, v_{2} = \frac{4 108}{6} - \frac{4 108}{6} i

Alternative Form

v_{1} \approx - 0.537285 + 0.537285 i, v_{2} \approx 0.537285 - 0.537285 i

Show Solution