Question

The principal argument of (sin 40° + i cos 40°)⁵ is ______ 

(a) -110° 

(b) -70° 

(c) 70°

(d) 110°

Answer 1

(a) -110°

(sin 40° + i cos 40°)⁵ 

= (cos 50° + i sin 50°)⁵

= (cos 250° + i sin 250°) 

250° lies in III quadrant. 

To find the principal argument the rotation must be in a clockwise direction which coincides with 250°

θ = -110°

Answer 2

(b) 0

 \(\int\limits_{0}^{1}\)(a - x)² f(x)dx 

= \(\int\limits_{0}^{1}\)(a² + x² -2ax) f(x)dx