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With these kind of problems you are looking to find 2 values with which the output of the function is positive for one and negative for the other. In this scenario they have given 2 values 2 and 3 so the ...

rearrange gives z = [(1+2i)^2]/(2+i)expanding (1+2i)^2 gives 4i-3 therefore this becomes (4i-3)/2+i multiply that by the conjugate (2-i)/(2-i) to give (11i-2)/5therefore z= -2/5 + 11i/5

Markscheme:[M1] correct expansion shown, allowing sign slips.[A1] correct (unsimplified) expression obtained [A1] correct answer obtained (this can also earn both A1 marks if correct expression is not sho...

We can use the characteristic equation, det(A - kI) = 0 to find the eigenvalues of A. Performing this, we see that(2-k) * ( (1-k)(3-k) - 3 ) = 0.Immediately, we can see a root is k = 2, which is ...

Using implicit differentiation, let y equal arccos(x) : y=arccos(x). So x = cos(y), and dx/dy = -sin(y). dy/dx is therefore -1/sin(y). from trig indentities: sin(y) = sqrt(1-cos^2(y)). Substituting gives ...