\left\{ \begin{array} { l } { - 1 = a _ { 1 } \cdot q ^ { 8 } } \\ { - 32 = a _ { 1 } \cdot q ^ { 12 } } \end{array} \right.
Solve for a_1, q (complex solution)
a_{1}=-\frac{1}{1024}=-0.000976562\text{, }q=2^{\frac{5}{4}}\approx 2.37841423
a_{1}=-\frac{1}{1024}=-0.000976562\text{, }q=\sqrt[4]{2}\times \left(2i\right)\approx 2.37841423i
a_{1}=-\frac{1}{1024}=-0.000976562\text{, }q=-2^{\frac{5}{4}}\approx -2.37841423
a_{1}=-\frac{1}{1024}=-0.000976562\text{, }q=-\sqrt[4]{2}\times \left(2i\right)\approx -0-2.37841423i
Solve for a_1, q
a_{1}=-\frac{1}{1024}=-0.000976562\text{, }q=-2^{\frac{5}{4}}\approx -2.37841423
a_{1}=-\frac{1}{1024}=-0.000976562\text{, }q=2^{\frac{5}{4}}\approx 2.37841423
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