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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
7583 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
5558 Views

Give two reasons why cryolite is used in the electrolysis of aluminium oxide.

The mixture of cryolite and aluminium oxide has a lower melting point than pure aluminium oxide. This means a lower amount of energy is required to establish effective conditions for electrolysis and thus...

JE
Answered by Javier E. • Chemistry tutor
87138 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
3532 Views

The lattice enthalpies of calcium oxide and magnesium oxide are different. Comment on this difference.

Differences in size of an ionic lattice are directly linked to differences in how exothermic the lattice enthalpy of a salt is. 

Mg2+ has a smaller radius than Ca2+  and thus ...

JE
Answered by Javier E. • Chemistry tutor
16152 Views

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