Prove that tan <mrow class="MJX-TeXAtom-ORD"> &#x2212;<!-- − --> 1

Sappeycuii

Sappeycuii

Answered question

2022-05-13

Prove that tan 1 1 5 π 16 using complex number method

Answer & Explanation

aliasjuliankso9y

aliasjuliankso9y

Beginner2022-05-14Added 11 answers

( 5 + i ) 4 = 476 + 480 i Since 476 is approximately 480, the angle of the line from 0 to 476+480i made with the x-axis is about 45 degrees or π / 4 radians.
So arctan ( 1 / 5 ) is about π / 4 4 or π / 16
Matilda Webb

Matilda Webb

Beginner2022-05-15Added 3 answers

We may notice that
(1) ( 5 + i ) 8 = 3824 + 456960 i
is a complex number relatively close to the imaginary axis. By applying arg to both sides of (1),
(2) 8 arctan 1 5 π 2
follows.

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