Express √3 + i in polar form:
|√3 + i| = √((√3)² + 1²) = √4 = 2
arg(√3 + i) = arctan(1/√3) = π/6
Then
√3 + i = 2 (cos(π/6) + i sin(π/6))
By DeMoivre's theorem,
(√3 + i)³ = (2 (cos(π/6) + i sin(π/6)))³
… = 2³ (cos(3 • π/6) + i sin(3 • π/6))
… = 8 (cos(π/2) + i sin(π/2))
… = 8i
Answer:
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Step-by-step explanation:
Answer:
Step-by-step explanation:
by inspection
angles 2 and 3 are equal, so they will be half angle ABC
angles 1 and 5 are equal so they will be
angle 1 + angle 5 + angleABC = 180° kind of a rule for triangle
the sum of all angles - 180°
(angle 1) x 2 = 180° - 70°
angle 1 = 90° - 35°
angle 1 = 55° which equals angle 5
angle 4 is clearly a right angle 90°
DO the same procedure for the bottom triangle
angle 8 and 9 are half of angle ADC
angle 8 and 9 are half of 46°
both are 23°
angle 6 equals angle 7
2 ×angle 6 = 180° - 46°
angle 6 = 90° - 23°
angle 6 = 67° angle 7 = 67°
Did I find them all
