Solve z-2=z^2(1-i)

Question

Solve the equation

z_{1} \approx - 0.155443 + 1.329066 i, z_{2} \approx 0.655443 - 0.829066 i

Evaluate

z - 2 = z^{2} (1 - i)

Use the commutative property to reorder the terms

z - 2 = (1 - i) z^{2}

Move the expression to the left side

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

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

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

Rewrite in standard form

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

Substitute a= - 1 + i,b= 1 and c= - 2 into the quadratic formula z = \frac{- b \pm b ^{2} - 4 a c}{2 a}

z = \frac{- 1 \pm 1 ^{2} - 4 ( - 1 + i ) ( - 2 )}{2 ( - 1 + i )}

Simplify the expression

z = \frac{- 1 \pm 1 ^{2} - 4 ( - 1 + i ) ( - 2 )}{- 2 + 2 i}

Simplify the expression

More Steps

z = \frac{- 1 \pm - 7 + 8 i}{- 2 + 2 i}

Simplify the radical expression

z = \frac{- 1 \pm ( 1.347246 + 2.969019 i )}{- 2 + 2 i}

Separate the equation into 2 possible cases

z = \frac{- 1 + 1.347246 + 2.969019 i}{- 2 + 2 i} z = \frac{- 1 - ( 1.347246 + 2.969019 i )}{- 2 + 2 i}

Simplify the expression

More Steps

z \approx 0.655443 - 0.829066 i z = \frac{- 1 - ( 1.347246 + 2.969019 i )}{- 2 + 2 i}

Simplify the expression

More Steps

z \approx 0.655443 - 0.829066 i z \approx - 0.155443 + 1.329066 i

Solution

z_{1} \approx - 0.155443 + 1.329066 i, z_{2} \approx 0.655443 - 0.829066 i

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