What is the answer to solvefor c,w+i= s/c ?

The answer to solvefor c,w+i= s/c is c=(ws)/(1+w^2)-s/(1+w^2)i

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solvefor c,w+i= s/c

solve for

c, w + i = \frac{s}{c}

c = \frac{w s}{1 + w ^{2}} - \frac{s}{1 + w ^{2}} i

Solution steps

w + i = \frac{s}{c}

Substitute

c = x + y i

w + i = \frac{s}{x + y i}

Multiply both sides by

x + y i

w (x + y i) + i (x + y i) = \frac{s}{x + y i} (x + y i)

Expand

w x - y + i (x + w y) = s

Rewrite

s

in standard complex form:

s + 0 i

w x - y + i (x + w y) = s + 0 i

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

[w x - y = s x + w y = 0]

[w x - y = s x + w y = 0] : x = \frac{w s}{1 + w ^{2}}, y = - \frac{s}{1 + w ^{2}}, w \neq = i, w \neq = - i, w \neq = 0

Substitute back

c = x + y i

c = \frac{w s}{1 + w ^{2}} - \frac{s}{1 + w ^{2}} i

6 i - x + y i = 4 + 2 i

∣ z ∣ - z = 2 + i

x, x^{2} y^{2} + x sin (y) = 4

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

z^{2} - (1 + 4 i) z - (5 + i) = 0

What is the answer to solvefor c,w+i= s/c ?
The answer to solvefor c,w+i= s/c is c=(ws)/(1+w^2)-s/(1+w^2)i