Question

The value of ${\left[\sin \left(\log i^i\right)\right]}^4+{\left[\sin \left(\log i^i\right)\right]}^5$

• A. $1$
• B. $-1$
• C. $2$1
• D. $0$

Answer 1

Answer: (D)

$0$

$w={\left[\sin \left(\log i^i\right)\right]}^4+{\left[\sin \left(\log i^i\right)\right]}^5$ ...(1)
Let $\theta =\log i^i=i\log i=i\log e^{i\frac{\pi }{2}}=i^2\frac{\pi }{2}=-\frac{\pi }{2}$
Substitute in eq. (1), we get

$\Rightarrow w={\left[\sin (-\frac{\pi }{2})\right]}^4+{\left[\sin (-\frac{\pi }{2})\right]}^5=1+(-1)=0$

Hence, option 'D' is correct.