What is the answer to i/z =-6 ?

The answer to i/z =-6 is z=-1/6 i

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i/z =-6

\frac{i}{z} = - 6

z = - \frac{1}{6} i

Solution steps

\frac{i}{z} = - 6

Substitute

z = x + y i

\frac{i}{x + y i} = - 6

Multiply both sides by

x + y i

\frac{i}{x + y i} (x + y i) = - 6 (x + y i)

Expand

i = - 6 x - 6 i y

Rewrite

i

in standard complex form:

0 + i

0 + i = - 6 x - 6 i y

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

[0 = - 6 x 1 = - 6 y]

[0 = - 6 x 1 = - 6 y] : x = 0, y = - \frac{1}{6}

Substitute back

z = x + y i

z = - \frac{1}{6} i

z - \frac{1}{z} = 4 + 3 i

∣ i + z ∣^{2} - i - 2 = z

a^{2} = i

i x^{2} + (1 - 2 i) x + 3 i - 1 = 0

x - 2 i = 2 + y i