What is the answer to i=(57)/(98+j50.894) ?

The answer to i=(57)/(98+j50.894) is j=-49000/25447-28500/25447 i

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i=(57)/(98+j50.894)

i = \frac{57}{98 + j 50.894}

j = - \frac{49000}{25447} - \frac{28500}{25447} i

Solution steps

i = \frac{57}{98 + j \cdot 50.894}

Substitute

j = x + y i

i = \frac{57}{98 + ( x + y i ) \cdot 50.894}

Multiply both sides by

98 + 50.894 x + 50.894 i y

i (98 + 50.894 x + 50.894 i y) = \frac{57}{98 + ( x + y i ) \cdot 50.894} (98 + 50.894 x + 50.894 i y)

Expand

- 50.894 y + i (98 + 50.894 x) = 57

Rewrite

57

in standard complex form:

57 + 0 i

- 50.894 y + i (98 + 50.894 x) = 57 + 0 i

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

[- 50.894 y = 57 98 + 50.894 x = 0]

[- 50.894 y = 57 98 + 50.894 x = 0] : x = - \frac{49000}{25447}, y = - \frac{28500}{25447}

Substitute back

j = x + y i

j = - \frac{49000}{25447} - \frac{28500}{25447} i

(x + i)^{2} = y

x + i y + 3 = 6 - 5 i

x + y i = (1 + i) + (2 + i)

z, z^{2} - 2 z + i = 0

(i 2 j^{3} k) \cdot (- ijk) = 0

What is the answer to i=(57)/(98+j50.894) ?
The answer to i=(57)/(98+j50.894) is j=-49000/25447-28500/25447 i