What is the answer to |z|-z=1+0i ?

The answer to |z|-z=1+0i is z=-1/2

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|z|-z=1+0i

∣ z ∣ - z = 1 + 0 i

z = - \frac{1}{2}

Decimal Notation

z = - 0.5

Solution steps

∣ z ∣ - z = 1 + 0 i

Substitute

z = x + y i

∣ (x + y i) ∣ - (x + y i) = 1 + 0 i

Expand

(x^{2} + y^{2} - x) - i y = 1

Rewrite

1

in standard complex form:

1 + 0 i

(x^{2} + y^{2} - x) - i y = 1 + 0 i

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[x^{2} + y^{2} - x = 1 - y = 0]

[x^{2} + y^{2} - x = 1 - y = 0] : (x = - \frac{1}{2}, y = 0)

Substitute back

z = x + y i

z = - \frac{1}{2}

x, z = x^{2} + i

3 (5 + bi) + 2 i = 2 a - 7 i

s i P (x) = 2 x - 1, Q (x) = x + 3

2 x - y + (2 x - 3 y - i) i = 0

(a + bi)^{2} + 4 (a + bi) = - 4 - 2 i