Solve m^22-i^41 - ScanMath

Question

Simplify the expression

2 m^{2} - 1

Evaluate

m^{2} \times 2 - i^{4} \times 1

Evaluate the power

More Steps

Evaluate

i^{4}

Calculate

i^{2} \times i^{2}

Calculate

(- 1) (- 1)

Calculate

1

m^{2} \times 2 - 1 \times 1

Use the commutative property to reorder the terms

2 m^{2} - 1 \times 1

Solution

2 m^{2} - 1

Show Solution

m_{1} = - \frac{2}{2}, m_{2} = \frac{2}{2}

Alternative Form

m_{1} \approx - 0.707107, m_{2} \approx 0.707107

Evaluate

m^{2} \times 2 - i^{4} \times 1

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

m^{2} \times 2 - i^{4} \times 1 = 0

Evaluate the power

More Steps

Evaluate

i^{4}

Calculate

i^{2} \times i^{2}

Calculate

(- 1) (- 1)

Calculate

1

m^{2} \times 2 - 1 \times 1 = 0

Use the commutative property to reorder the terms

2 m^{2} - 1 \times 1 = 0

Any expression multiplied by 1 remains the same

2 m^{2} - 1 = 0

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

2 m^{2} = 0 + 1

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

2 m^{2} = 1

Divide both sides

\frac{2 m ^{2}}{2} = \frac{1}{2}

Divide the numbers

m^{2} = \frac{1}{2}

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

m = \pm \frac{1}{2}

Simplify the expression

More Steps

Evaluate

\frac{1}{2}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{1}{2}

Simplify the radical expression

\frac{1}{2}

Multiply by the Conjugate

\frac{2}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{2}{2}

m = \pm \frac{2}{2}

Separate the equation into 2 possible cases

m = \frac{2}{2} m = - \frac{2}{2}

Solution

m_{1} = - \frac{2}{2}, m_{2} = \frac{2}{2}

Alternative Form

m_{1} \approx - 0.707107, m_{2} \approx 0.707107

Show Solution