Express ${{\left( 3-\mathrm{i} \right)}^{2}}$ in the form of $a+\mathrm{i}b$.[1] Hence or otherw

Question

Express ${{\left( 3-\mathrm{i} \right)}^{2}}$ in the form of $a+\mathrm{i}b$.[1] Hence or otherwise find the roots of the equation ${{\left( z+\mathrm{i} \right)}^{2}}=-8+6\mathrm{i}$.[3] Given that ${{z}_{1}}=2-4\mathbf{i}$ and ${{z}_{2}}=-2-\mathbf{i}$, find $\left| {{z}_{1}}-{{z}_{2}} \right|$. [2] $\arg ({{z}_{1}}+{{z}_{2}})$. [2]

Accepted Answer

$\text{(a)}\ (3-\mathbf{i})^2=8-6\mathbf{i},\quad z=1+2\mathbf{i}\ \text{or}\ -1-4\mathbf{i}$ $\text{(b)(i)}\ 5$ $\text{(b)(ii)}\ -\dfrac{\pi}{2}$

N2004 P1 Q12

N2004 P1 Q12

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