What is derivative of (x+2i)(y+2i)=-1+8i ?

The answer to derivative of (x+2i)(y+2i)=-1+8i is (dy)/(dx)=(-4-xy)/(4+x^2)+i(-2x+2y)/(4+x^2)

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derivative of (x+2i)(y+2i)=-1+8i

derivative of

(x + 2 i) (y + 2 i) = - 1 + 8 i

\frac{d y}{d x} = \frac{- 4 - x y}{4 + x ^{2}} + i \frac{- 2 x + 2 y}{4 + x ^{2}}

Solution steps

(x + 2 i) (y + 2 i) = - 1 + 8 i

Treat

y

y (x)

Differentiate both sides:

(x \frac{d y}{d x} + y) + i (2 + 2 \frac{d y}{d x}) = 0

Isolate

\frac{d y}{d x} : \frac{d y}{d x} = \frac{- 4 - x y}{4 + x ^{2}} + i \frac{- 2 x + 2 y}{4 + x ^{2}}

\frac{d y}{d x} = \frac{- 4 - x y}{4 + x ^{2}} + i \frac{- 2 x + 2 y}{4 + x ^{2}}

x^{2} + y^{2} = 1

2 x + 25 y = 0

x^{2} y + y^{2} x = 6

x^{2} (x - 2 y) = x + 2 y

p = i^{2} r

What is derivative of (x+2i)(y+2i)=-1+8i ?
The answer to derivative of (x+2i)(y+2i)=-1+8i is (dy)/(dx)=(-4-xy)/(4+x^2)+i(-2x+2y)/(4+x^2)