Prove e^(ix) = cos (x) + isin(x)

MYTUTOR SUBJECT ANSWERS

Answers / Further Mathematics / A Level / Prove e^(ix) = cos (x) + isin(x)

728 views

Prove e^(ix) = cos (x) + isin(x)

We first write each side of the equation using the maclaurin series for each function.

e^ix = 1 + ix + (ix)²/2! + (ix)³/3! + (ix)⁴/4! + ......

e^ix = 1 + ix - x²/2! - ix³/3! + x⁴/4! + .....

cos(x) + isin(x) = (1 - x²/2! + x⁴/4! - x⁶/6! +....) + i(x - x³/3! + x⁵/5! - x⁷/7! + ......)

writing the above equation in increasing powers of x:

cos(x) + isin(x) = 1 + ix - x²/2! - ix³/3! + x⁴/4! + ....

As seen the maclaurin series for each side of the equation are the same hence e^ix = cos(x) + isin(x)

Pavan M. A Level Maths tutor, A Level Further Mathematics tutor, Uni...

2 years ago

Answered by Pavan, who has applied to tutor A Level Further Mathematics with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

121 SUBJECT SPECIALISTS

Scott R. GCSE Maths tutor, 13 Plus Maths tutor, A Level Maths tutor,...

View profile

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Further Mathematics , Maths

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

5.0

36 reviews | 96 completed tutorials

Save profile

Joshua B. GCSE Maths tutor, A Level Maths tutor, A Level Further Math...

View profile

£26 /hr

Joshua B.

Degree: Mathematics (Masters) - Durham University

Subjects offered:Further Mathematics , Maths

“Hi! I’m Josh, a third year on a four-year Mathematics course. I got 100% in both my Maths IGCSE and A-Level, and did all 18 A-Level modules.”

4.9

129 reviews | 205 completed tutorials

Save profile

Ellie B. GCSE Maths tutor, 11 Plus Maths tutor, A Level Maths tutor, ...

View profile

£26 /hr

Ellie B.

Degree: Mathematics (Masters) - York University

Subjects offered:Further Mathematics , Physics+ 1 more

“I study Maths at York University; I chose York because I loved the lecturers, they made maths fun and easy- that's what I hope to do with all my students!”

5.2