Solve |z| = z*z^-1 - ScanMath

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Type your math problem... |z| = z*z^-1

x

Question

Solve the equation

z_{1} = - 1, z_{2} = 1

Evaluate

∣ z ∣ = z \times z^{- 1}

Find the domain

∣ z ∣ = z \times z^{- 1}, z \neq = 0

Multiply the terms

More Steps

Evaluate

z \times z^{- 1}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

z^{1 - 1}

Subtract the numbers

z^{0}

Any non-zero expression raised to the power of 0 equals 1

1

∣ z ∣ = 1

Separate the equation into 2 possible cases

z = 1 z = - 1

Check if the solution is in the defined range

z = 1 z = - 1, z \neq = 0

Find the intersection of the solution and the defined range

z = 1 z = - 1

Solution

z_{1} = - 1, z_{2} = 1

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