Question

Evaluate: \(\rm 2+\sqrt2i\over3-\sqrt2i\)

1. \(\rm {4\over11}+{5\sqrt2\over11}i\)
2. \(\rm {4\over11}-{\sqrt2\over11}i\)
3. \(\rm {4\over11}-{5\sqrt2\over11}i\)
4. \(\rm {4\over11}+{\sqrt2\over11}i\)

Answer 1

Correct Answer - Option 1 : \(\rm {4\over11}+{5\sqrt2\over11}i\)

Calculation:

z = \(\rm 2+\sqrt2i\over3-\sqrt2i\)

z = \(\rm {2+\sqrt2i\over3-\sqrt2i}\times{3+\sqrt2i\over3+\sqrt2i}\)

z = \(\rm {6+5\sqrt2i-2\over3^2-(\sqrt2i)^2}\)

z = \(\rm {4+5\sqrt2i\over9-(-2)}\)

z = \(\rm {4\over11}+{5\sqrt2\over11}i\)