Find the result of the following operation: (frac{2 + 3i}{1 - 2i}). Then, rationalize the denominator using complex conjugates.

Question

Accepted Answer

Step:1 ：(frac{2 + 3i}{1 - 2i} times frac{1 + 2i}{1 + 2i} = frac{(2 + 3i)(1 + 2i)}{(1 - 2i)(1 + 2i)})Step:2 ：(= frac{2 + 4i + 3i + 6i^2}{1 - 4i^2})Step:3 ：(= frac{2 + 7i - 6}{1 + 4} = frac{-4 + 7i}{5})Step:4 ：(= -frac{4}{5} + frac{7}{5}i)

Answer

Step: 1 ：(frac{2 + 3i}{1 - 2i} times frac{1 + 2i}{1 + 2i} = frac{(2 + 3i)(1 + 2i)}{(1 - 2i)(1 + 2i)})Step: 2 ：(= frac{2 + 4i + 3i + 6i^2}{1 - 4i^2})Step: 3 ：(= frac{2 + 7i - 6}{1 + 4} = frac{-4 + 7i}{5})Step: 4 ：(= -frac{4}{5} + frac{7}{5}i)

Find the result of the following operation: \(\frac{2 + 3i}{1 - 2i}\). Then, rationalize the denominator using complex conjugates.

Answer

Popular Problems