Mathematics, 07.07.2019 20:10 cherryy

Match each expression to its equivalent standard form.

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Answer from: Rakeem458

(x+1+i)(x+1-i) goes with x^2+2x+2

(x+2i)(x-2i) goes with x^2+4

(x-2+2i)(x-2-2i) goes with x^2-4x+8

Step-by-step explanation:

(x+1+i)(x+1-i)

(x+[1+i])(x+[1-i])

Use foil.

First: x(x)=x^2

Outer: x(1+i)=x+ix

Inner: x(1-i)=x-ix

Last: (1+i)(1-i)=1-i^2 since 1+i and 1-i are conjugates

__Add together to get: x^2+2x+1-i^2

We can actually simplify this because i^2=-1

So x^2+2x+1-i^2=x^2+2x+1-(-1)=x^2+2x+2

(x+2i)(x-2i)

These are conjugates so just do first and last of foil.

First: x(x)=x^2

Last: 2i(-2i)=-4i^2=-4(-1)=4

==Adding together gives x^2+4

(x-2+2i)(x-2-2i)

(x+[-2+2i])(x+[-2-2i])

This is similar to first.

Foil time!

First: x(x)=x^2

Outer: x(-2-2i)=-2x-2ix

Inner: x(-2+2i)=-2x+2ix

Last: (-2-2i)(-2+2i)=4-4i^2 (multiplying conjugates again)

==Add together giving us x^2-4x+4-4i^2

This can be simplified since i^2=-1.

So applying this gives us x^2-4x+4-4(-1)

=x^2-4x+4+4

=x^2-4x+8

Answer from: roseemariehunter12

1. The first expression is equivalent to x^2+2x+2 .

2. The second expression is equivalent to x^2+4 .

3. The third expression is equivalent to x^2-4x+8 .

Step-by-step explanation:

(1).

The given expression is

(x+1+i)(x+1-i)

[(x+1)+i][(x+1)-i]

Using the algebraic properties, we get

(x+1)^2-(i)^2 $[\because a^2-b^2=(a-b)(a+b)]$

x^2+2x+1-(i)^2 $[\because (a+b)^2=a^2+2ab+b^2]$

x^2+2x+1-(-1) $[\because i^2=-1]$

x^2+2x+2

Therefore the first expression is equivalent to x^2+2x+2 .

(2).

The given expression is

(x+2i)(x-2i)

Using the algebraic properties, we get

(x)^2-(2i)^2 $[\because a^2-b^2=(a-b)(a+b)]$

x^2-4i^2

x^2-4(-1) $[\because i^2=-1][/tex[tex]x^2+4$

Therefore the second expression is equivalent to

x^2+4 .

(3)

The given expression is

(x-2+2i)(x-2-2i)

[(x-2)+2i][(x-2)-2i]

Using the algebraic properties, we get

(x-2)^2-(2i)^2 $[\because a^2-b^2=(a-b)(a+b)]$

x^2-4x+4-4i^2 $[\because (a-b)^2=a^2-2ab+b^2]$

x^2-4x+4-4(-1) $[\because i^2=-1]$

x^2-4x+4+4

x^2-4x+8

Therefore the third expression is equivalent to x^2-4x+8 .

Answer from: Quest

i cant see the graph

step-by-step explanation:

Answer from: Quest

3x + 18 = 147°

step-by-step explanation:

3x + 18 = 147°, because the value of the central angle is equal to the value of the arc formed by it.

i hope i you.

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Match each expression to its equivalent standard form.
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