Real part of ( cos 4 + i sin 4 + 1 ) 2020 is_______

Step-by-step solution

Given, ( cos 4 + i sin 4 + 1 ) 2020 Now using, 1 + cos 2 A = 2 cos 2 A and sin 2 A = 2 sin A cos A , we get 2 cos 2 2 + 2 i sin 2 cos 2 2020 ⇒ 2 cos 2 cos 2 + i sin 2 2020 Now, By using De Moivre's Theorem, we get ⇒ 2 2020 cos 2020 2 cos 2 × 2020 + i sin 2 × 2020 ⇒ 2 2020 cos 2020 2 cos 4040 + i sin 4040 Hence, the Real part is 2 2020 cos 2020 2 cos 4040