Expand (3 + 2i)² with the identity (a + b)² = a² + 2ab + b²…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Expand with the identity . Then check by multiplying term by term. Finally, factorise with complex numbers.
Need a reminder? The key ideaShow
Add and take away part by part. Multiply out the brackets and put for : . The commutative, associative and distributive laws hold, and so do all the algebraic identities.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. The identity. .
Step 2. Term by term. . The two ways agree.
Step 3. Factorise. .
Answer: , and .
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