What is the answer to -6i=(-i)/(120pi*C) ?

The answer to -6i=(-i)/(120pi*C) is C= 1/(720pi)

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-6i=(-i)/(120pi*C)

- 6 i = \frac{- i}{120 π \cdot C}

C = \frac{1}{720 π}

Decimal Notation

C = 0.00044 \dots

Solution steps

- 6 i = \frac{- i}{120 π C}

Substitute

C = x + y i

- 6 i = \frac{- i}{120 π ( x + y i )}

Multiply both sides by

120 π x + 120 πi y

- 6 i (120 π x + 120 πi y) = \frac{- i}{120 π ( x + y i )} (120 π x + 120 πi y)

Expand

720 π y - 720 πi x = - i

Rewrite

- i

in standard complex form:

0 - i

720 π y - 720 πi x = 0 - i

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

[720 π y = 0 - 720 π x = - 1]

[720 π y = 0 - 720 π x = - 1] : x = \frac{1}{720 π}, y = 0

Substitute back

C = x + y i

C = \frac{1}{720 π}

(x + y i) (2 + i) = 6 - 2 i

x^{2} = - \frac{4}{3} i

22 x - 3 y i = 3 y i + 2 x

(1 + i) (a + bi) - 2 (a - bi) = - 11 + 25 i

(1 + i) (a + 2 b) - (3 - 2 i) (a - b) = 8 + 3 i

What is the answer to -6i=(-i)/(120pi*C) ?
The answer to -6i=(-i)/(120pi*C) is C= 1/(720pi)