What is the answer to |z-1|=1 ?

The answer to |z-1|=1 is z=0\lor z=2

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|z-1|=1

∣ z - 1 ∣ = 1

z = 0 or z = 2

Solution steps

∣ z - 1 ∣ = 1

Apply absolute rule: If

∣ u ∣ = a, a > 0

then

u = a

u = - a

z - 1 = - 1 or z - 1 = 1

z - 1 = - 1 or z - 1 = 1

z = 0 or z = 2

6 (x - 5) = 4 x + 20

x^{2} + 3 x + 5 x + 15

6 x - 3 (x + 8) = 9

\frac{\frac{1}{y} - \frac{1}{x}}{\frac{1}{x ^{2}} + \frac{1}{y ^{2}}}

9^{3} \cdot 9^{3}