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For part i this is what I did: let z=x+iy New Equation: |x+i(y-2)|=y (x^2 +(y-2)^2 )^(1/2)=y x^2 + (y-2)^2 =y^2 x^2 + y^2 -4y +4=y^2 4y=x^2 + 4 y= (x^2)/4 +1 I know this is different from my initial equation (I found where I made a mistake), but could you explain what is wrong with that...

(i) Find the equation of the locus of z given |z-2i|=Im(z) (ii) Find the maximum and minimum values of argz (iii) Find z in the form a+ib when argz takes its minimum value I could do (i) and my answer was y=(x^2)/2 +2, but I couldn't complete ii or iii Any help would be appreciated

The complex number z satisfies the equation arg(z+2)=pi/3 (i) Sketch the locus of the point P that represents z (ii) Hence find the equation of the locus of P (iii)Hence find the minimum value of |z-3| I have completed i and ii, just don't have a clue on iii Any help would be appreciated

Step 1) Prove for n=8 LHS:2^8=256 RHS: 3(8)^2=192, therefore 2^n>3n^2 is true for n=8 Step 2) Assume true for n=k ie 2^k>3k^2 Step 3) Prove for n=k+1 from step 2, 2^k>3k^2 therefore, 2(2^k)>2(3k^2) therefore, 2^(k+1)>6k^2 therefore, 2^(k+1)>3(k+1)^2+3k^2-6k-3>3(k+1)^2 [as (3k^2-6k-3) is...

Find the area shaded which is bound by the curve y=e^x, the line y=e and the y axis

Hey, I am doing an essay on postmodernism and my thesis is that postmodernism does not offer any alternatives when critiquing texts. Does anyone know any good texts to support this thesis?

yeh sorry it was pq=-1

x=2(p+q) y=p^(3)+q^(3)

I meant tan 22.5

Using (1-tanx)/1+tanx)=tan(45-x) Find tan 22(x/2)

Prove: (2cos(x/2)-1-cosx)/(<meta charset="utf-8">2cos(x/2)+1+cosx)=(1-cos(x/2))/(1+cos(x/2))