STATEMENT-1-z-1-2-z-2-2-z-3-2-z-4-2-0-where-z-1-z-2-z-3-and-z-4-are-the-fourth-roots-of-unity-and-STATEMENT-2-1-1-4-cos0-i-sin0-1-4-

Tinku Tara June 4, 2023 Algebra 0 Comments

Question Number 21111 by Tinkutara last updated on 13/Sep/17

STATEMENT-1 : z_1 ^2 + z_2 ^2 + z_3 ^2 + z_4 ^2 = 0 where z_1 , z_2 , z_3 and z_4 are the fourth roots of unity. and STATEMENT-2 : (1)^(1/4) = (cos0° + i sin0°)^(1/4) .

$$\mathrm{STATEMENT}-\mathrm{1}\::\:{z}_{\mathrm{1}} ^{\mathrm{2}} \:+\:{z}_{\mathrm{2}} ^{\mathrm{2}} \:+\:{z}_{\mathrm{3}} ^{\mathrm{2}} \:+\:{z}_{\mathrm{4}} ^{\mathrm{2}} \:= \\ $$$$\mathrm{0}\:\mathrm{where}\:{z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} ,\:{z}_{\mathrm{3}} \:\mathrm{and}\:{z}_{\mathrm{4}} \:\mathrm{are}\:\mathrm{the}\:\mathrm{fourth} \\ $$$$\mathrm{roots}\:\mathrm{of}\:\mathrm{unity}. \\ $$$$\boldsymbol{\mathrm{and}} \\ $$$$\mathrm{STATEMENT}-\mathrm{2}\::\:\left(\mathrm{1}\right)^{\frac{\mathrm{1}}{\mathrm{4}}} \:=\:\left(\mathrm{cos0}°\:+\right. \\ $$$$\left.{i}\:\mathrm{sin0}°\right)^{\frac{\mathrm{1}}{\mathrm{4}}} . \\ $$

Facebook Tweet Pin

STATEMENT-1-z-1-2-z-2-2-z-3-2-z-4-2-0-where-z-1-z-2-z-3-and-z-4-are-the-fourth-roots-of-unity-and-STATEMENT-2-1-1-4-cos0-i-sin0-1-4-

Leave a Reply Cancel reply