0

Guest

Courses New

(1+cos( π/7)+isin ( π/7)) 14 = ? how to get answer........................................................

(1+cos(π/7)+isin(π/7))14= ?
how to get answer........................................................
 

Grade:10

1 Answers

Damith Dilhan
17 Points
5 years ago
We can use e^{i\theta} form for this problem where,
Cos(\theta)+iSin(\theta) =e^{i\theta}
Before that we have to remove 1 from equation.In order to do that we substitute1+Cos(\pi/7)=2cos^{2}(\pi/14) and Sin(\pi/7)=2sin(\pi/14)cos(\pi/14),
Then,
(1+cos(\pi /7)+isin(\pi/7))^{14}=(2cos^{2}(\pi/14)+i2sin(\pi/14)cos(\pi/14))^{14}(2cos^{2}(\pi/14)+i2sin(\pi/14)cos(\pi/14))^{14}=2^{14}cos^{14}(\pi/14)(cos(\pi/14)+isin(\pi/14))^{14}2^{14}cos^{14}(\pi/14)(cos(\pi/14)+isin(\pi/14))^{14}=2^{14}cos^{14}(\pi/14)(e^{i\pi/14})^{14}2^{14}cos^{14}(\pi/14)(e^{i\pi/14})^{14}=2^{14}cos^{14}(\pi/14)e^{i\pi}2^{14}cos^{14}(\pi/14)e^{i\pi}=2^{14}cos^{14}(\pi/14)(cos(\pi)+isin(\pi))2^{14}cos^{14}(\pi/14)(cos(\pi)+isin(\pi))=16382.24*(-1)=-16382.24

Think You Can Provide A Better Answer ?

Other Related Questions on Algebra

View all Questions »

ASK QUESTION

Get your questions answered by the expert for free

Answer and earn gift vouchers

Win Gift vouchers upto Rs 500/-

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Click Here Know More

Complete Self Study Package designed by Industry Leading Experts

Click Here Know More

Live 1-1 coding classes to unleash the Creator in your Child

Click Here Know More

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Click Here Know More