Question

Simplify the given expression:

4 divided by the quantity of 3 minus 2i

HELP!!!! MEDAL!!!!

Answer 1

you mean

\[\frac{ 4 }{ 3-2i }\]

Answer 2

?

Answer 3

I'm not going to do the exercise for you. You can only learn when working together

Answer 4

YES AND I WILL

Answer 5

???

Answer 6

So my question is whether what you need to simplify looks like what I wrote in my first reply

Answer 7

YES it is

Answer 8

Ok. What does i stand for?

Answer 9

do not say just says simplify

Answer 10

i is the complex number... i²=-1 and so i is the square of -1. It is not a variable. It is the symbol for something that does not exist with the real numbers. In the Real numbers you cannot take the square of a negative number. But with the Complex numbers you can because -1 = i² and you can always write the square of i² as i.

This means that if you were to have to take the square of -9 you could also write it as 9.(-1) or as 9i². You can take the square from that, which will be 3i.

So all these simplify questions have as a purpose to teach you how to work with the complex number i and i² and -1. Do you understand now what i means?

Answer 11

I understand

Answer 12

Ok so we could write the exercise in another way so that you can understand why you need to simplify it, and perhaps recognize how you need to simplify it.

\[\frac{ 4 }{ 3-2i }=\frac{ 4 }{ 3-2\sqrt{-1} }\]

Have you learned what you should do if there is a square root in the denominator?

Answer 13

no

Answer 14

when you have a squareroot you want to get rid of it in the denominator. Instead it will appear in the numenator, but that's less bad than in the denominator.

Example:
Let's say you have
\[\frac{ 5 }{ ? }\]

You can "simplify" it (that means getting rid of the square root in the denominator) by doing this:

\[\frac{ 5 }{ \sqrt{2} }\frac{ \sqrt{2} }{ \sqrt{2} }=\frac{5\sqrt{2}}{2}\]

Multiplying a square root of a number with itself cancels out the square root.

Example two:
\[\frac{ 5 }{ 1+\sqrt{2} }\]

You "simplify" it by doing this

\[\frac{ 5 }{ 1+\sqrt{2} }\frac{ 1-\sqrt{2} }{ 1-\sqrt{2} }=\frac{5(1-\sqrt{2})}{1-2}=\frac{5(1-\sqrt{2})}{-1}= -5(1-\sqrt{2})\]

Important: you have take the opposite sign when multiplying a denominator like that. Because then you have a remarkable product of (a+b)(a-b)=(a²-b²).

So when there is an i in the denominator is like having a square root in the denominator, because i= squareroot of -1.

So, you need to do what with the original expression?

Answer 15

sorry the first expression should be

\[\frac{ 5 }{ \sqrt{2} }\]

not

\[\frac{ 5 }{ ? }\]