In the complex set C, the solution of the equation | x | + x = 1 + 3I is | Math enthusiast | Mathematical art

In the complex set C, the solution of the equation | x | + x = 1 + 3I is

Let x = a + bi, then √ (a ^ 2 + B ^ 2) + A + bi = 1 + 3I, [√ (a ^ 2 + B ^ 2) + A-1] + (B-3) I = 0
So, B-3 = 0, √ (a ^ 2 + B ^ 2) + A-1 = 0, the solution is: B = 3, a = - 4
Therefore, the solution of the equation | x | + x = 1 + 3I is x = - 4 + 3I

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