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Expand (3 + 2i)² with the identity (a + b)² = a² + 2ab + b².

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

Expand $(3 + 2i)^2$ with the identity $(a + b)^2 = a^2 + 2ab + b^2$ . Then check by multiplying $(3 + 2i)(3 + 2i)$ term by term. Finally, factorise $p^2 + 25$ with complex numbers.

Need a reminder? The key ideaShow

Add and take away part by part. Multiply out the brackets and put $-1$ for $i^2$ : $(a + ib)(c + id) = (ac - bd) + i(ad + bc)$ . The commutative, associative and distributive laws hold, and so do all the algebraic identities.

The worked solution

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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.

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Expand (3 + 2i)² with the identity (a + b)² = a² + 2ab + b².

The worked solution

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