What is the answer to z-2x+7-6i=0 ?

The answer to z-2x+7-6i=0 is z=(2x-7)+6i

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z-2x+7-6i=0

z - 2 x + 7 - 6 i = 0

z = (2 x - 7) + 6 i

Solution steps

z - 2 x + 7 - 6 i = 0

Substitute

z = a + bi

a + bi - 2 x + 7 - 6 i = 0

Rewrite

a + bi - 2 x + 7 - 6 i

in standard complex form:

(a - 2 x + 7) + (b - 6) i

(a - 2 x + 7) + (b - 6) i = 0

Rewrite

0

in standard complex form:

0 + 0 i

(a - 2 x + 7) + (b - 6) i = 0 + 0 i

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

[a - 2 x + 7 = 0 b - 6 = 0]

[a - 2 x + 7 = 0 b - 6 = 0] : (x \in R, a = 2 x - 7, b = 6)

Substitute back

z = a + bi

z = (2 x - 7) + 6 i

3 + 8 i = x + y i

∣ z - 3 i ∣ = 3

∣ z - 3 i ∣ = 5

y = in (2 x), y, y = 1, y = 6

x^{2} - 2 x + i = 0