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Geometric Intuition of Multiplying Complex Numbers

Multiplying Complex Numbers

So we have just seen that multiplying by real numbers causes a rotation of either or and multiplying by causes a rotation of so now lets see what happens when we multiply by other complex numbers... If you have a go at the activity below you will find that multiplying by different complex numbers causes a rotation of of lots of angles. Notice as well that the vector is also scaled with each multiplication like before. The question is, how can we determine the amount of rotation and scaling from the complex number? This is what we will explore in more detail in the next few sections...