Melody

don't you like my big brain Rosala   

There is no conjugate on the second one compare it to surds for it is much the same

rationalize the denominator

$$\\\frac{6}{2\sqrt5}=\frac{6}{2\sqrt5}\times\frac{\sqrt5}{\sqrt5}=
\frac{6\sqrt5}{2*5}=\frac{6\sqrt5}{10}=\frac{3\sqrt5}{5}\\\\\\
BUT\\\\
\frac{6}{2+\sqrt5}=\frac{6}{2+\sqrt5}\times\frac{2-\sqrt5}{2-\sqrt5}=\;\;etc$$

1)   

$$\\\frac{1-i}{3i}\times\frac{i}{i}=\frac{(1-i)i}{3i^2}=\frac{i-i^2}{3*-1}=
\frac{i--1}{-3}=\frac{i+1}{-3}=\frac{-1-i}{3}=-\frac{1}{3}-\frac{i}{3}$$

Yes, i learned this trick from Heureka too.  It really is neat.  Thanks Heureka 

Just google it - it will probably be quicker.   Click on images that is usually quicker still  

Hi Nagendra,

Welcome to Web2.calc forum.   

I hope that you like it here.    

Thank you for your big effort.  Unfortunately it was not correct.  Please look at my solution and learn from it, then next time you are much more likely to get it correct.  :)  

I shall give you 3 points to get you started and for you effort.

-11x+4+8x+-4+3x

=-11x+4+8x-4+3x

=-11x+8x+3x      +4-4

=-11x+8x+3x       because 4-4=0

=-11x+    11x

=0

Always remember that you can only add like terms.   Sometimes when adding and subtracting it can be very useful to think of the letters as things.

S you can think of this as -11 xylophones + the number 4 +8 xylophones - the number 4 +3 xylophones

You can put all the xylophones together and as a seperate issue you can put the numbers together.  

Thanks Heureka   

You draw a right angled triangle

sec is hyp/adjacent

so mark one acute angle as theta

mark the hyp as 7 and the adj as 4  Use Pythagoras's theorem to work out the opposite side.

Now read all the ratios straight from the triangle.

8 to the power of 4/3 =

$$\\8^{\frac{4}{3}}=\left(8^{\frac{1}{3}}\right)^4=\left(\sqrt[3]{8}\right)^4=2^4=16$$