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the answer is 5/9

the two images would look like 

ik it looks out of shape but it would look something like this

 

I have no idea what "T 2n 1" and "T 2n 4" mean ...

Yes the gradient and the slope are the same thing.

To divide two complex numbers, multiply both the numerator and the denominator of the fraction by the

conjugate of the denominator.

The conjugate of the complex number  a + bi  is the complex number  a - bi.

Denominator:  -1 + 5i     --->     Conjugate:  -1 - 5i

[ (2 - 3i) / (-1 + 5i) ]  · [ (-1 - 5i) / (-1 - 5i) ]  =  [ (2 - 3i) · (-1 - 5i) ]  /  [ (-1 + 5i) · (-1 - 5i) ]

Now, you'll need to multiply:  (2 - 3i) · (-1 - 5i)          [this will be the numerator of your answer]

and   you'll need to multiply:  (-1 + 5i) · (-1 - 5i)        [this will be the denominator of your answer]

The denominator will no longer contain any "i" terms; it will just be a regular, real, number.

Looks like you start with one block and then keep adding a column of 4 blocks.

So can you draw the next to pics?

What would they look like?

Yes, I can see you tried and that is good progress. I appreciate your effort.

The photos (for the pic) were ok, you just need to work out how to get them the right way around.   :)

Your pic just changed but there is no indication that you edited, how did that happen?  That is a bit weird.

Anyway, your pic looks much better now.  I assume it is now correct?

And also, is the gradient the slope?

Ok, sorry for my answer format. Will do next time!

Sorry for the late response and long answer...I made an error in my explanation and had to correct it!

Let's break the sum of two numbers down to see if we can find a pattern:
 

\(17^1+15^1=32\) The highest power of 2 that can divide this is 32 or \(2^5\)
\(17^2+15^2=514\) The highest power of 2 that can divide this is 2 or \(2^1 \)

\(17^3+15^3=8288\) The highest power of 2 that can divide this is 32 or \(2^5 \)

\(17^4+15^4=134146\) The highest power of 2 that can divide this is 2 or \(2^1\)

Here you can see a pattern, the largest power of 2 that can divide the sum is either \(2^5\) or \(2^1\). You can also see that when the exponents in the sum are odd, the sum is divisible by \(2^5\) but when the exponents of the sum are even, the sum is divisible by \(2^1\). 

In the sum of the numbers above, their exponents are 2 apart. 

\(17^3+15^1=4928\) The highest power of 2 that can divide this is 64 or \(2^6\)

\(17^4+15^2=83746\) The highest power of 2 that can divide this is 2 or \(2^1\)

\(17^5+15^3=1423232\) The highest power of 2 that can divide this is 128 or \(2^7\)

\(17^6+15^4=24188194\) The highest power 2 that can divide this is 2 or \(2^1\)

\(17^7+15^5=411098048\) The highest power of 2 that can divide this is 64 or \(2^6\)

This pattern is different, but we can see that every other odd exponent in the sum has \(2^6\) as the largest power of 2 divisor. 

Based on this pattern, \({17}^{17}+{15}^{15}\), the largest divisor that is a power of 2 is \(2^7\).

The modulus of the complex number  a + bi  =  sqrt( a² + b² ).

For  - 2 + 8i  the modulus is  sqrt( (-2)² + (8)² )  =  sqrt( 4 + 64 )  =  sqrt( 68 )  or  3·sqrt( 17 ).

If you multiply  -2 + 8I  by  5  you get  5(-2 + 8i)  =  -10 + 40i.

Now, you need to find the modulus of this complex number, place it into reduced radical form, and compare it to the

answer above.

To answer in what quadrant you find the original number and the new number, plot both  -2 + 8i  and  -10 + 40i

and answer the question:  Are they in the same quadrant?  If not, what is the location of the second number in

relation to the location of the first number?

Is that what your pic is supposed to look like?

Two complex numbers: c+di and e+fi.

The product is (c+di)(e+fi) = ce+cfi+dei+dfi^2 = (ce-df)+i(cf+de)

Can you go from here?

You are very welcome!

:P

The correct rectangular equivalene of 3sqrt(2)·cis( 7pi/4 ) is:

     3sqrt(2)·cos( 7pi/4 ) + i·sqrt(2)·sin( 7pi/4 )  =  3 - 3i

As to what he did wrong: he probably interchanged the sin function and the cos function when he was doing

the problem or interchanged the values for sin and cos.

Hi Helpmeee,

You can see that the slope is -2 but peepee obviously cannot.

Peepee can copy your answer but he/she cannot learn from it.

Try leading an asker like this, without just giving them an answer to copy.

For example, you could have asked peepee what the y-intercept and the gradient is.  Then waited for a response before you went further.

From the graph, we can tell that the slope is -2 and the y-intercept is -3. From this we can write the equation y = -2x-3. From here we can change this equation into standard form: 2x + y = -3 

The universe?

You could start by presenting your question better.

I understand your points and I see what you're talking about a lot. But I'm not the person to down vote because I don't like someone. In fact, I upvoted your thread because it brings up a valid point. The only problem is that I don't know what this can do. From the time you've made your first post on this thread, I've already seen many people post questions that are obviously their homework or something of the kind. Instead of being angry at this a more proactive path might be to brainstorm ideas on how to counter-act this.

Thanks so much! That looks like a lot of work, I really appreciate it! Have a good day :D

Thanks! But I'm kind of confused. . .  what do you mean since there's more variables than equations there will be infinite soultions?

Please don't take this the wrong way, I don't doubt that it's correct, I'm just wondering why :)

Have a chill good day! (darn I did it again. . . )