Another way to look at it is as a single circle at the origin and consider the distances to the points 2 and -2. When t=π/2, the sum of the distances takes on a certain value, and all other points with the same sum lie on an ellipse with foci at 2 and -2. We know π/2 must maximise the sum because all other points on the circle lie inside that ellipse.
Another approach is observing the fact that sum of squared distance of any point in that circle ( of radius 1) from 2 and -2 is always 10. You can verify this in polar form or rearrangement of the circle equation, then as (a+b)^2 =2(a^2+b^2)-(a-b)^2 so it will be maximum when a=b or both the distance are same. The last part can also be done by finding max value of ab using AM GM inequality .
Fantastic questions for development pattern recognition, and connecting imaginary numbers with distantance, using basic problem solving skill of introducing something simpler. Did student like the lesson, or was this complete pulling couple student above sea water lever(so to speak)? Anyways I tutor mathematics, and your videos are very helpful, short and to the point, and lost of reason to stay alert.
![The most beautiful equation in math, explained visually [Euler’s Formula]](http://i.ytimg.com/vi/f8CXG7dS-D0/mqdefault.jpg)
Another way to look at it is as a single circle at the origin and consider the distances to the points 2 and -2. When t=π/2, the sum of the distances takes on a certain value, and all other points with the same sum lie on an ellipse with foci at 2 and -2. We know π/2 must maximise the sum because all other points on the circle lie inside that ellipse.
Another approach is observing the fact that sum of squared distance of any point in that circle ( of radius 1) from 2 and -2 is always 10. You can verify this in polar form or rearrangement of the circle equation, then as (a+b)^2 =2(a^2+b^2)-(a-b)^2 so it will be maximum when a=b or both the distance are same. The last part can also be done by finding max value of ab using AM GM inequality .
Best maths teacher in the world 🌍👍👍
Very good explanation 👌💯
Amazing, it all makes sense now! Thanks
Convert the expression form euiler form to polar form and then it's very easy
It will take not more than 30 sec
Fantastic questions for development pattern recognition, and connecting imaginary numbers with distantance, using basic problem solving skill of introducing something simpler. Did student like the lesson, or was this complete pulling couple student above sea water lever(so to speak)? Anyways I tutor mathematics, and your videos are very helpful, short and to the point, and lost of reason to stay alert.
Amazing sir.YOU can't miss the maths and science tutorials. hurry and check it out. THANKS
genius
would -2 be a shift to the right because its actually z-(a+ib)
Solved in less than 30 sec
👍👍👍👍