Question

Perform the indicated operation.

(-9 + 2i) - (-12 + 4i) =

Answer 1

You can drop the first set of parentheses because they are unnecessary.
To get rid of the second set of parentheses, you need to distribute the negative sign.

Example: -(2x - 6) = -2x + 6

Answer 2

Then add like terms.

Answer 3

so its 3-2i?

Answer 4

can i keep you for a few more questions?

Answer 5

Correct.

Answer 6

(-9 + 2i) - (-12 + 4i) =
= -9 + 2i + 12 - 4i
= -9 + 12 + 2i - 4i
= 3 - 2i

Answer 7

The product of a complex number and its conjugate is always
A)
real.
B)
imaginary.
C)
rational.
D)
natural.

Answer 8

Do you know what the conjugate of a complex number is?

Answer 9

nope

Answer 10

Ok, let's start there.

Answer 11

For a complex number a + bi, its complex conjugate is a - bi.
This is very simple. The complex conjugate of a complex number is another complex number in which all you do is change the sign of the imaginary part (the part with the i).

Answer 12

so the answer i its real

Answer 13

is

Answer 14

Examples:

Complex Number Complex Conjugate
5 + 3i 5 - 3i
-4 + 2i -4 - 2i
6 - i 6 + i
-2 - 3i -2 + 3i
5 5

Answer 15

Correct, but do you know why?

Answer 16

because adding to real numbers together always give you real numbers?

Answer 17

You're not adding them. You are multiplying a complex number and its conjugate.

Answer 18

ok cool

Answer 19

Select the BEST classification for π.
A)
irrational
Eliminate
B)
rational
C)
imaginary
D)
complex

Answer 20

is this one irrational

Answer 21

Let's use the general complex number a + bi. Let's even say that b is not zero. this way the number does have its imaginary part. The complex conjugate of a + bi is a - bi.

Now we multiply a + bi by its complex conjugate:

(a + bi)(a - bi)
Notice that this is the product of a sum and a difference.
It follows the pattern: \((x + y)(x - y) = x^2 - y^2\)
(If you forgot this pattern, you can always use FOIL and collect like terms.)

We can use the pattern.

\(a + bi)(a - bi)\)

\( = a^2 - (bi)^2 \)

\(= a^2 - b^2i^2\)

\(= a^2 - i^2b^2\), but \(i^2 = -1\), so

\(= a^2 - (-1)b^2\)

\(= a^2 + b^2\)

As you can see there is no i in the final expression, so \(a^2 + b^2\), the product of a complex number and its complex conjugate, is a real number.

Answer 22

Correct, \(\pi\) is irrational.

Answer 23

oh it makes sence now

Answer 24

(x
1
a

)(x
1
b

)
Write the expression in simplified radical form.

Answer 25

Great.

Answer 26

Sorry, gtg.

Answer 27

oh ok thank you!!