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If z=4+i, what is 1/z? (in the form a+bi)

1/z =1/(4+i) Multiply both top and bottom by the complex conjugate, z* = 4 - i, 1/z = (4-i)/((4+i)(4-i)) = (4-i)/(16+4i-4i-i 2 ) = (4-i)/17 ans: 4/17 - i/17
RH
3604 Views

Find the stationary point of 3x^2+7x

dy/dx=6x+7 6x+7=0 x=-7/6 Sub back into original equation; y=98/6
HS
3028 Views

Factorise the following quadratic x^2 - 8 + 16

Find two numbers that multiply together to equal the 3rd term and the product of the same two numbers also needs to equal the 2nd term. This is trial and error but in this case it will be, (x - 4) (x - 4)
AJ
2986 Views

How would I solve the following equation d^2x/dt^2 + 5dx/dt + 6x = 0

Our given equation is d 2 x/dt 2 + 5dx/dt + 6x = 0, which we need to recognise as a second order differential equation. Therefore we need to begin by solving the auxilary funtion m 2 +5m +6= 0. ( Side note: ...
DM
6821 Views

write showing all working the following algebraic expression as a single fraction in its simplest form: 4-[(x+3)/ ((x^2 +5x +6)/(x-2))]

4-[(x+3)*((x-2)/(x^2 +5x +6))] 4-[(x+3)(x-2)/(x^2 +5x +6))] factorise denominator 4-[(x+3)(x-2)/(x+3)(x+2)] cancel down (x+3) 4-[(x-2)/(x+2)] expand 4(x+2)/(x+2) - (x-2)/(x+2) now share a denominator so make...
ST
12783 Views