Use de Moivre’s theorem to write the following complex numbers in the form a+ib.
Note that for these questions arguments of complex numbers lie in the range -\pi\lt \arg \le \pi.
Enter all answers rounded to 3 decimal places.
Important: When calculating the final answer to each question, you must use the full calculator values for the modulus and argument calculated in the first two parts and not the rounded values, otherwise the final answer will not be guaranteed to be correct to 3 decimal places.
a)
(2.7+1.2i)^{−1}
\begin{split} \text{i.} & \left\lvert (2.7 + 1.2i)^{-1} \right\rvert = \input \\ \text{ii.} & \arg\bigl((2.7+1.2i)^{−1}\bigr) = \input \\ \text{iii.} & \text{So } (2.7+1.2i)^{-1}=\input \end{split}
b)
(1.6+2.3i)^{−1}
\begin{split} \text{i.} & \left\lvert (1.6+2.3i)^{−1} \right\rvert = \input \\ \text{ii.} & \arg\bigl((1.6+2.3i)^{−1}\bigr) = \input \\ \text{iii.} & \text{So } (1.6+2.3i)^{−1}=\input \end{split}
c)
(1.5+i)^{−1}
\begin{split} \text{i.} & \left\lvert (1.5+i)^{−1} \right\rvert = \input \\ \text{ii.} & \arg\bigl((1.5+i)^{−1}\bigr) = \input \\ \text{iii.} & \text{So } (1.5+i)^{−1}=\input \end{split}