Question

separate real and imaginary parts of tan(1+i)​

Answer 1

Answer:

Given:

• z = tan (1 + i)

Solution:

tan (a + b) = (tan a + tan b) / (1 - tan a tan b)

» tan (1 + i) = (tan 1 + tan i) / (1 - tan 1 tan 1i)

On rationalizing the denominator

= (tan 1 + tan i) (1 + tan 1 tan i) / (1 + tan⁴1)

= (tan 1 + i tan³1 + tani - tan³1) / (1 + tan⁴1)

= (tan 1 - tan³1) / (1 + tan⁴1) + (i tan³1 + tani) / (1 + tan⁴1)

Now, comparing with real and imaginary parts

Real part = (tan 1 - tan³1) / (1 + tan⁴1)

Imaginary part = (i tan³1 + tani) / (1 + tan⁴1)