Find Three Ordered Pair Solutions f(z)=z^2-2+2i

$f (z) = z^{2} - 2 + 2 i$

Step 1

Write $f (z) = z^{2} - 2 + 2 i$ as an equation.

$y = z^{2} - 2 + 2 i$

Step 2

Choose any value for $z$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $z$ to find the ordered pair.

Remove parentheses.

$y = 0^{2} - 2 + 2 i$

Remove parentheses.

$y = {(0)}^{2} - 2 + 2 i$

Simplify ${(0)}^{2} - 2 + 2 i$ .

Raising $0$ to any positive power yields $0$ .

$y = 0 - 2 + 2 i$

Subtract $2$ from $0$ .

$y = - 2 + 2 i$

Use the $z$ and $y$ values to form the ordered pair.

$(0, - 2 + 2 i)$

Step 4

Choose $1$ to substitute in for $z$ to find the ordered pair.

Remove parentheses.

$y = 1^{2} - 2 + 2 i$

Remove parentheses.

$y = {(1)}^{2} - 2 + 2 i$

Simplify ${(1)}^{2} - 2 + 2 i$ .

One to any power is one.

$y = 1 - 2 + 2 i$

Subtract $2$ from $1$ .

$y = - 1 + 2 i$

Use the $z$ and $y$ values to form the ordered pair.

$(1, - 1 + 2 i)$

Step 5

Choose $2$ to substitute in for $z$ to find the ordered pair.

Remove parentheses.

$y = 2^{2} - 2 + 2 i$

Remove parentheses.

$y = {(2)}^{2} - 2 + 2 i$

Simplify ${(2)}^{2} - 2 + 2 i$ .

Raise $2$ to the power of $2$ .

$y = 4 - 2 + 2 i$

Subtract $2$ from $4$ .

$y = 2 + 2 i$

Use the $z$ and $y$ values to form the ordered pair.

$(2, 2 + 2 i)$

Step 6

These are three possible solutions to the equation.

$(0, - 2 + 2 i), (1, - 1 + 2 i), (2, 2 + 2 i)$

Step 7

Find Three Ordered Pair Solutions f(z)=z^2-2+2i

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