Year 11 Maths - Specialist Complex numbers

Multiplication and division of complex numbers

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Questions

Question 1

56732

Expand and simplify

i) $(3-2i)^2$

ii) $(5+3i)(5-3i)$

Answer

i) $5-12i$ ii) $34$

Worked Solution

$$\begin{aligned}
&\begin{aligned}\text{(i)}\quad
(3-2 i)^{2} &=(3-2 i)(3-2 i) \\ &=3(3-2 i)-2 i(3-2 i) \\ &=9-6 i-6 i-4 \\ &=5-12 i
\end{aligned}\\
&\begin{aligned}\text{(i)}\quad (5+3 i)(5-3 i) &=5(5-3 i)+3 i(5-3 i) \\ &=25-15 i+15 i+9 \\ &=34
\end{aligned}
\end{aligned}$$

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