What do you think? What does the student know, what misconception might they have, and how would you help them?
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First Year in Maths · A network for academics teaching mathematics in first-year degree programs
I’ll start us off!
It looks like the student knows what the conjugate ‘bar’ symbol means and also knows that they need to multiply a fraction by the demonimator’s conjugate. Unfortunately, they do not seem to understand the reason for the need to multiply the demonimator by the conjugate as the demonimator still contains complex numbers.
There is a significant misconception with multiplying and dividing complex numbers. It seems that when expanding brackets and simplying the fraction, this student has multiplied/divided real parts together and then mulitplied/divided imaginary parts together.
It might be worth giving the same student some simple expand problems such as (a+2)(a-4) to see if they think expanding brackets always becomes a^2-8, or if they believe it only applies to complex numbers.