What is the answer to z=z(a+i) ?

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z=z(a+i)

z = z (a + i)

z = 0

Solution steps

z = z (a + i)

Substitute

z = x + y i

x + y i = (x + y i) (a + i)

Expand

(x + y i) (a + i) : (a x - y) + i (x + a y)

x + y i = (a x - y) + i (x + a y)

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

[x = a x - y y = x + a y]

[x = a x - y y = x + a y] : (a \in R, x = 0, y = 0)

Substitute back

z = x + y i

z = 0

\frac{x + 1 + i ( y - 3 )}{5 + 3 i} = 1 + i

v \cdot v = i - 5 j

0 = z + \frac{i}{z}

15 - 28 = 3 l + (4 m) i

+ 4 i z^{2} = 2 + 2 i, z^{1} = 7