What is the answer to 10^3= i/(io) ?

The answer to 10^3= i/(io) is o= 1/1000

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10^3= i/(io)

1 0^{3} = \frac{i}{i o}

o = \frac{1}{1000}

Decimal Notation

o = 0.001

Solution steps

1 0^{3} = \frac{i}{i o}

Substitute

o = x + y i

1 0^{3} = \frac{i}{i ( x + y i )}

Multiply both sides by

i (x + y i)

1 0^{3} i (x + y i) = \frac{i}{i ( x + y i )} i (x + y i)

Simplify

- 1000 y + 1000 i x = i

Rewrite

i

in standard complex form:

0 + i

- 1000 y + 1000 i x = 0 + i

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

[- 1000 y = 0 1000 x = 1]

[- 1000 y = 0 1000 x = 1] : x = \frac{1}{1000}, y = 0

Substitute back

o = x + y i

o = \frac{1}{1000}

a + ib = 3 + 2 i

- 0.008647 i = \frac{1}{x \cdot i}

x^{2} - y^{2} + x i - y i = 21 + 3 i

z^{2} = - 4 - 2 i

\frac{( 2 + ai )}{1 + i} = re a l