Complex trigo

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LongLifeLearner

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Oct 23, 2020
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Asked to solve a given complex number equation cos z = -i sin z + i, where z=x+iy.

I tried use defination of complex trigonometric sin z & cos z & also it identities but get no wsy. Where should i start with this kind of question? Tq
 
LongLifeLearner said:
Asked to solve a given complex number equation cos z = -i sin z + i, where z=x+iy.

I tried use defination of complex trigonometric sin z & cos z & also it identities but get no wsy. Where should i start with this kind of question? Tq
Click to expand...
Apply D'Moivre's Theorem?

If you don't know D'Moivre's Theorem - look in your textbook/class-notes and do a Google search. Please come back and tell us what you found?
 
Subhotosh Khan said:
Apply D'Moivre's Theorem?

If you don't know D'Moivre's Theorem - look in your textbook/class-notes and do a Google search. Please come back and tell us what you found?
Click to expand...

De Moivre come across before but i thought it only use to solve equation with power. Anyhow after get the advice, i tried again and yes finally i get it.

I rearranged the equation become cos z +isin z = i, and i rewrite it into form of euler and compare both side. Thanks sir.
 
LongLifeLearner said:
De Moivre come across before but i thought it only use to solve equation with power. Anyhow after get the advice, i tried again and yes finally i get it.

I rearranged the equation become cos z +isin z = i, and i rewrite it into form of euler and compare both side. Thanks sir.
Click to expand...
You could have solved it here.

cos z +isin z = i → cos(z) = 0 and sin(z) = 1

z = (4k+1)/2 * π + i * 0
 
Subhotosh Khan said:
Apply D'Moivre's Theorem?

If you don't know D'Moivre's Theorem - look in your textbook/class-notes and do a Google search. Please come back and tell us what you found?
Click to expand...

Sir how about this:

Cos z + 2i sin z=3i? I tried use the same method but can't get it
 
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