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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...

Answered by Jihoon K. • Maths tutor

7207 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: 9^3x+1=3^y

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

Answered by Judy G. • Maths tutor

5183 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
3253 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
2954 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
6278 Views

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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 .

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

What is the Product Rule?

How do I use Pythagoras?

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

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