Question

the real part of sin(x+iy)​

Answer 1

Their is no real part.

When we will expand sin(x+iy)

we get sinxcosiy + cosxsiniy

So no term is without iota

Answer 2

The real part of sin(x+iy) is sinx coshy

Given :

sin(x+iy)

To find :

The real part of sin(x+iy)

Solution :

Step 1 of 3 :

Write down the given expression

The given expression is sin(x+iy)

Step 2 of 3 :

Simplify the given expression

$\sf sin(x + iy)$

$\sf = sinx \: cosiy \: + cosx \: siniy$

$\sf = sinx \: coshy \: + icosx \: sinhy$

Step 3 of 3 :

Find real part

Real part = sinx coshy

Imaginary part = cosx sinhy

Hence real part of sin(x+iy) = sinx coshy

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