Complex Conjugates

[nycmathguy]

Section 2.4
40 & 42

Question 40

8 - 10i

The complex conjugate is 8 + 10i.

(8 - 10i) (10 + 10i)

80 + 80i - 80i - 100i^2

80 - 100(-1)

80 + 100 = 180

Question 42

-3 + sqrt{2}i

The complex conjugate is -3 - sqrt{2}.

(-3 + sqrt{2})(-3 - sqrt{2})

9 + 3sqrt{2} - 3sqrt{2} - sqrt{4}

9 - 2 = 7

You say?

I see that 44 and 46 do not include the variable I. Can you do 44 and 46?

 

[MathLover1]

40.

(8 - 10i) (10 + 10i)

80 + 80i - 80i - 100i^2-> mistake : instead of -80i should be -100i

80 + 80i - 100i - 100(-1)

80 - 20i +100

180 - 20i
20(9 - i )

& 42 is correct


44.

If
x≥0, then sqrt(x ) means the non-negative square root of x
.
If x<0 then sqrt(x)=sqrt(-x)*i

So sqrt(-15)=sqrt(15)*i

so the complex conjugate is -sqrt(15)*i

then (sqrt(15)*i)(-sqrt(15)*i)=15


46.

complex conjugate conjugate is

where

since

then

and complex conjugate is

then product of

=

=

=

 

[nycmathguy]

40.

(8 - 10i) (10 + 10i)

80 + 80i - 80i - 100i^2-> mistake : instead of -80i should be -100i

80 + 80i - 100i - 100(-1)

80 - 20i +100

180 - 20i
20(9 - i )

& 42 is correct


44.

If
x≥0, then sqrt(x ) means the non-negative square root of x
.
If x<0 then sqrt(x)=sqrt(-x)*i

So sqrt(-15)=sqrt(15)*i

so the complex conjugate is -sqrt(15)*i

then (sqrt(15)*i)(-sqrt(15)*i)=15


46.

complex conjugate conjugate is

where

since

then

and complex conjugate is

then product of

=

=

=

Very nice work. Thanks for the correction as pointed out. With this we end Section 2.4. We move on to Section 2.5 or Zeros of Polynomial Functions.