What is the answer to z+zbar=5i+6 ?

The answer to z+zbar=5i+6 is z= 6/(1+bar)+5/(1+bar)i

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z+zbar=5i+6

z + z ba r = 5 i + 6

z = \frac{6}{1 + ba r} + \frac{5}{1 + ba r} i

Solution steps

z + z ba r = 5 i + 6

Substitute

z = x + y i

x + y i + (x + y i) ba r = 5 i + 6

Rewrite

x + y i + (x + y i) ba r

in standard complex form:

(x + ba r x) + (y + ba ry) i

(x + ba r x) + (y + ba ry) i = 5 i + 6

Rewrite

5 i + 6

in standard complex form:

6 + 5 i

(x + ba r x) + (y + ba ry) i = 6 + 5 i

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

[x + ba r x = 6 y + ba ry = 5]

[x + ba r x = 6 y + ba ry = 5] : x = \frac{6}{1 + ba r}, y = \frac{5}{1 + ba r}, b \neq = - \frac{1}{a r}

Substitute back

z = x + y i

z = \frac{6}{1 + ba r} + \frac{5}{1 + ba r} i

a + 2 bi + 3 = 5 - 4 i

\frac{z ^{2} - i}{z - 2} = 2

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

(1 + i) x + (- 2 + i) y = - 3 + 16 i

24 + 42 y i = - 0.5 x + 0.5 i

What is the answer to z+zbar=5i+6 ?
The answer to z+zbar=5i+6 is z= 6/(1+bar)+5/(1+bar)i