What is the answer to 0.022i= 1/(x*i) ?

The answer to 0.022i= 1/(x*i) is x=-500/11

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0.022i= 1/(x*i)

0.022 i = \frac{1}{x \cdot i}

x = - \frac{500}{11}

Decimal Notation

x = - 45.45454 \dots

Solution steps

0.022 i = \frac{1}{x i}

Substitute

x = a + bi

0.022 i = \frac{1}{( a + bi ) i}

Multiply both sides by

(a + bi) i

0.022 i (a + bi) i = \frac{1}{( a + bi ) i} (a + bi) i

Expand

- 0.022 a - 0.022 ib = 1

Rewrite

1

in standard complex form:

1 + 0 i

- 0.022 a - 0.022 ib = 1 + 0 i

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

[- 0.022 a = 1 - 0.022 b = 0]

[- 0.022 a = 1 - 0.022 b = 0] : a = - \frac{500}{11}, b = 0

Substitute back

x = a + bi

x = - \frac{500}{11}

3 x + 4 y + (x + 2 y) i = 5 + 3 i

r (t) = (5 + t) i + t j

a, z = \frac{1 - ai}{1 + ai}

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

(2 + i) x + 7 y = 1 + 2 i, (1 - i) x - i y = 4 - i

What is the answer to 0.022i= 1/(x*i) ?
The answer to 0.022i= 1/(x*i) is x=-500/11