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Let w, z be complex numbers. Show that |wz|=|w||z|, and using the fact that x=|x|e^{arg(x)i}, show further that arg(wz)=arg(w)+arg(z) where |.| is the absolute value and arg(.) is the angle (in polar coordinates). Hence, find all solutions to x^n=1 .

Put w=a+bi, z=c+di where a, b, c, d are real, and i2=-1. Then |wz|2=|(a+bi)(c+di)|2=|ac-bd+(ad+cb)i|2=(ac)2+(bd)2-2bcd+(ad)2+(c...

JK
Answered by Jihoon K. • Maths tutor
7594 Views

Express 9^(3x+)1 in the form 3^y giving y in the form of ax+b where a and b are constants.

Fistly show that: 93x+1=3y

To find x we need to get the left hand side of the equation to be 3m(3x+1) where 3m

JG
Answered by Judy G. • Maths tutor
5565 Views

What is the Product Rule?

The product rule is used when differentiating two functions that are multiplied by eachother. The formula for the product rule is: 

U (dv/dx) + V (du/dx)    where 'dv/dx' is the differential of the...

AW
Answered by Abbie W. • Maths tutor
3550 Views

How do I use Pythagoras?

Pythagoras theorum is used to identify the lengths of any side on a right angle triangle. The theorem is as follows:

a2  + b2 = c2    

We assume that the hyp...

AW
Answered by Abbie W. • Maths tutor
3283 Views

A book was reduced by 35% in a sale. It's new price is £16. What was the original price ?

Begin by looking at the percentage reduction: 

100% - 35% = 65%

Therefore, 65% = £16 (as this was the price it was reduced to)

1% = £16 ÷ 65 = 0.2462

So to find the ...

DW
Answered by David W. • Maths tutor
6767 Views

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