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.