Complex Analysis: Polar Form

Bring it all to three dimensions. The short video points out that the discussion in the previous presentations in two dimensions also holds true for three dimensions. The sixth video in the series of 15 specifically makes the connections...

Represent complex numbers in two ways. Pupils use the interactive to convert polar and rectangular representations of complex numbers. The learners drag an overlay back and forth over the coordinate plane to reveal the polar coordinates...

Fight against the current. Pupils explore the resulting path when they are crossing a river while being pushed downstream by the current. Using vector notation, learners express the speed and direction of a ferry. They finish by...

Translate vectors to find equivalent ones. An interactive shows 10 randomly displayed vectors. Pupils grab the vectors and move them to group them with similar vectors in magnitude and direction. Scholars find the groups of vectors that...

Move vectors to determine their difference. Pupils use an interactive to visualize the opposite of a vector. They use the concept of adding vectors to subtract vectors by adding the opposite and, finally, view the differences of the...

View vector addition with a greater magnitude. The interactive provides learners with the opportunity to determine the magnitude of vectors and their resultant vectors when added. Pupils investigate the relationship between the...

Find out if vectors are equal in the classroom. Pupils use the interactive to create vectors showing the movements boys perform in rearranging classroom furniture. The scholars determine which boy moved furniture the farthest, or if they...

Find the right number of vectors to get to the finish line. Using a boat race scenario, pupils add multiples of the same vector together. The scholars use scalar multiplication to speed up the boats in an exciting race to the finish. 

Two words summarize the interactive: vector projector. An easy-to-use resource lets users investigate vector projections on the coordinate plane. Given the components of two vectors, they determine the projection of one vector onto the...

Find the location of enemy submarines with a sonar display that doubles as a polar coordinate system. Pupils find polar coordinates that would be the same location of plotted submarines. They then determine multiple polar coordinates...