Degree 3; zeros: 1,1-i

Answered question

2022-04-04

Degree 3; zeros: 1,1-i

Answer & Explanation

alenahelenash

alenahelenash

Expert2022-06-06Added 556 answers

f(x)=(x-1)(x-(1-i))(x-(1+i))

Simplify each term.

Apply the distributive property.

f(x)=(x-1)(x-11+i)(x-(1+i))

Multiply -1 by 1.

f(x)=(x-1)(x-1+i)(x-(1+i))

Multiply -1 by -1.

f(x)=(x-1)(x-1+1i)(x-(1+i))

Multiply i by 1.

f(x)=(x-1)(x-1+i)(x-(1+i))

Expand (x-1)(x-1+i) by multiplying each term in the first expression by each term in the second expression.

f(x)=(xx+x-1+xi-1x-1-1-1i)(x-(1+i))

Simplify terms.

f(x)=(x2-x+xi-x+1-i)(x-(1+i))

Subtract x from -x.

f(x)=(x2+xi-2x+1-i)(x-(1+i))

Simplify each term.

Apply the distributive property.

f(x)=(x2+xi-2x+1-i)(x-11-i)

Multiply -1 by 1.

f(x)=(x2+xi-2x+1-i)(x-1-i)

Expand (x2+xi-2x+1-i)(x-1-i) by multiplying each term in the first expression by each term in the second expression.

f(x)=x2x+x2-1+x2(-i)+xix+xi-1+xi(-i)-2xx-2x-1-2x(-i)+1x+1-1+1(-i)-ix-i-1-i(-i)

Simplify terms.

Simplify each term.

f(x)=x3-x2+x2(-i)+x2i-xi+x-2x2+2x+2xi+x-1-i-ix+i-1

Simplify by adding terms.

f(x)=x33x2+4x2

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