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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-i²) = (4-i)/17 ans: 4/17 - i/17

dy/dx=6x+7

6x+7=0

x=-7/6

Sub back into original equation; y=98/6

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 -...

Our given equation is d²x/dt² + 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^...

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+...