Question:
If z₁=\sqrt3+i\sqrt3 and z₂=\sqrt3+i, then the complex number
((z₁)/(z₂))⁵0
lies in the
If z₁=\sqrt3+i\sqrt3 and z₂=\sqrt3+i, then the complex number
((z₁)/(z₂))⁵0
lies in the
Show Hint
In powers of complex numbers, only the argument decides the quadrant.
Updated On: Mar 19, 2026
- first quadrant
- second quadrant
- third quadrant
- fourth quadrant
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The Correct Option is A
Solution and Explanation
Write in polar form:
z₁=2\sqrt3eⁱπ/4,
z₂=2eⁱπ/6
Thus,
((z₁)/(z₂))⁵0
=eⁱ⁵⁰⁽π/⁴⁻π/⁶⁾
=eⁱ⁽²⁵π⁾/⁽⁶⁾
This lies in the first quadrant.
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