What is the answer to 1/(iC)=-0.035i ?

The answer to 1/(iC)=-0.035i is C= 200/7

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1/(iC)=-0.035i

\frac{1}{i C} = - 0.035 i

C = \frac{200}{7}

Decimal Notation

C = 28.57142 \dots

Solution steps

\frac{1}{i C} = - 0.035 i

Substitute

C = x + y i

\frac{1}{i ( x + y i )} = - 0.035 i

Multiply both sides by

i (x + y i)

\frac{1}{i ( x + y i )} i (x + y i) = - 0.035 ii (x + y i)

Expand

1 = 0.035 x + 0.035 i y

Rewrite

1

in standard complex form:

1 + 0 i

1 + 0 i = 0.035 x + 0.035 i y

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

[1 = 0.035 x 0 = 0.035 y]

[1 = 0.035 x 0 = 0.035 y] : x = \frac{200}{7}, y = 0

Substitute back

C = x + y i

C = \frac{200}{7}

x + i y + i x + y = 2 + i

(3 x - 2 y i)^{2} = \frac{200}{4 + 3 i}

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

x^{2} = 16 i

x^{2} - x - i = 0