Anyone any good at Maths?

blue-army

Hi, just wondering would anyone be able to help...Pre's tomorrow :eek:...found a few Q's where I'm not really sure of the answer...Could someone maybe do them out?

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If a(2b + 3) = 3b - 4, express b in terms of a

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complex numbers
Let Z1 = 3 + 4i and z2 = 1 - 7i
(i) Find the value of the real number k such that Iz1I= k Iz2I

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a) if x= 1 over y + 2 over z, find the value of x when y=3 and z=4

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C) i) Write 1 over 4 cubed as a power of 2
ii)Solve the equation 2 to the power of 3x -15=1 over 4 cubed

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hope someone can help!

Thanks.

QueenOfLeon

blue-army wrote: »

Hi, just wondering would anyone be able to help...Pre's tomorrow :eek:...found a few Q's where I'm not really sure of the answer...Could someone maybe do them out?

---

If a(2b + 3) = 3b - 4, express b in terms of a

_

---

complex numbers
Let Z1 = 3 + 4i and z2 = 1 - 7i
(i) Find the value of the real number k such that Iz1I= k Iz2I

---

a) if x= 1 over y + 2 over z, find the value of x when y=3 and z=4

---

C) i) Write 1 over 4 cubed as a power of 2
ii)Solve the equation 2 to the power of 3x -15=1 over 4 cubed

---

hope someone can help!

Thanks.

1) If a(2b + 3) = 3b - 4, express b in terms of a
2ab +3a = 3b - 4
2ab - 3b = -4-3a
b(2a-3) = -4-3a
b = (-4-3a) over (2a-3)


Let Z1 = 3 + 4i and z2 = 1 - 7i
(i) Find the value of the real number k such that Iz1I= k Iz2I
(3+4i) = k(1-7i)
3+4i = k-7ki
Seperate real and imaginary
3=k and 4i=-7ki
k=3 -7k=4
k=-4over7

(im not 100% sure about this one...hopefully someone will correct me if im wrong)



a) if x= 1 over y + 2 over z, find the value of x when y=3 and z=4
x = (1 over 3) + (2 over 4)
x = (2 over 6) + (3 over 6)
x = (5 over 6)


C) i) Write 1 over 4 cubed as a power of 2
ii)Solve the equation 2 to the power of 3x -15=1 over 4 cubed
(i) (1 over 4) cubed = (2 to the power of 0x3) over (2 to the power of 2x3)
=(2 to the power of 0) over (2 to the power of 6)
= 2 to the power of (0 minus 6) (laws of indices)
= 2 to the power of -6

(ii) 2 to power of 3x - 15 = (1 over 4) cubed
2 to power of 3x - 15 = 2 to the power of -6 (previous answer)
3x - 15 = -6 you can cancel the 2s
3x = 9
x=3


Really hope i did all those right!! if you have a question about them let me know if i didnt do it clearly enough...its hard to type maths!!

Good luck with the mocks...mine start thursday

Cokehead Mother

For the complex numbers questions, it should be

|3 + 4i| = k|1 - 7i|

so

root[3^2 + 4^2] = k.root[1^2 + (-7)^2]

QueenOfLeon

Woops sorry could u explain that tho? i dont remember doing anything like that...and im in honours :eek::eek: some serious revision needed....

Cokehead Mother

|z| denotes the modulus/absolute value of the complex number of z.

Basically, if you plot the number on an argand diagram, the modulus is its distance from the the origin. So if z = a + bi, then |z| = root(a^2 + b^2) because of Pythagoras' theorem.

There's no real value of k such that (3+4i) = k(1-7i).

Gavin "shels"

If these are exam questions, all the marking schemes can be found on www.examinations.ie with the methods and what you get marks for.;)

blue-army

Gavin shels wrote: »

If these are exam questions, all the marking schemes can be found on www.examinations.ie with the methods and what you get marks for.;)

nah, not from the papers......


Thanks everyone!

Swizz

Good Luck to ya