Find the solution of Z² + |Z| = 0

Algebra Level 3

Find the solution of Z 2 + ∣ Z ∣ = 0 Z^2 + |Z| = 0 .

S = { 0 , i , − 1 } S = \{0, i, -1\} S = { 0 , i , − i } S = \{0, i, -i\} S = { 0 , 1 , − i } S = \{0, 1, -i \} S = { 0 , 1 , − 1 } S = \{0, 1, -1\}

Samuel Nascimento by Samuel Nascimento , 24, Brazil

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1 solution

Let Z = a + i b Z=a+ib ( a , b a, b are reals). Then from the given equation we get a = 0 a=0 , b 2 − ∣ b ∣ = 0 b^2-|b|=0 or b = 0 b=0 , a 2 + ∣ a ∣ = 0 a^2+|a|=0 . Therefore Z = 1 , Z = i , Z = − i Z=1, Z=i, Z=-i

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