lolcakes52
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- Oct 31, 2011
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- 2012
How do you type text without it becoming bunched up and how do you align your equals signs?
Show us the method that you used.Thanks for that. How would you do this question:
View attachment 24089
I could do it but the second part took me a bit of time whilst in the answers they just wrote it down with no working (past school paper). Am I missing something ridiculously simple?
Answer the second question using firstThanks for that. How would you do this question:
View attachment 24089
I could do it but the second part took me a bit of time whilst in the answers they just wrote it down with no working (past school paper). Am I missing something ridiculously simple?
Did you sketch the graph? That sometimes gives the answer away especially in complex number questions. However I don't think there is a quicker algebraic method but I could be wrong.The answer is pi/4. The way I did it was find the gradient of the line passing through the origin that was a tangent to the parabola since that would have the minimum argument of z and then used the fact that the gradient of a line equals the tangent of the argument to get pi/4. There must be some easier way though isn't there?
How did you use calculus for this problem?I considered that the arg(z)=tan^(-1)[y/x] and once I had the cartesian equation of the curve I just used calculus. Note that the curve is a parabola that is concave up and that the minimum clearly must occur in the first quadrant
It's good to see new methods pop up. I never thought of this. Nice work!arg(z)=tan^(-1)[y/x]=tan^(-1)[(x^2+4)/4x]. Let arg(z)=A.
Now, A=tan^(-1)[(x^2+4)/4x]
Differentiate with respect to x and set the derivative equal to 0 in order to find the point at which A is a minimum. You find that a minimum occurs at the point (2,2). Hence it follows that the minimum value for the arg(z)=tan^(-1)[2/2]=tan^(-1)[1]=pi/4
Better than being stuck and not thinking at allyeh lol, i couldnt think of anything else.