The value of Expression cos-2 - isin-2cos-22 - isin-22-to -is

(cosπ/2 + isinπ/2)(cosπ/2^2 + isinπ/2^2)...........to ∞ is = cos(π+ π/2 +π/2^2+.......) +isin(π+ π/2 +π/2^2+.......) =cosπ/2(1+ 1/2 +1/2^2+.......) +isinπ/2 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Properties with Negative X

The value of ...

Question

The value of Expression $(c o s \frac{π}{2} + i s i n \frac{π}{2})$

$(c o s \frac{π}{2^{2}} + i s i n \frac{π}{2^{2}})$ ...........to $\infty$ is

-1

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
-1

$(c o s \frac{π}{2} + i s i n \frac{π}{2})$ $(c o s \frac{π}{2^{2}} + i s i n \frac{π}{2^{2}})$ ...........to $\infty$ is

= cos $(π + \frac{π}{2} + \frac{π}{2^{2}} + . . . . . . .)$ +isin $(π + \frac{π}{2} + \frac{π}{2^{2}} + . . . . . . .)$

=cos $\frac{π}{2}$ $(1 + \frac{1}{2} + \frac{1}{2^{2}} + . . . . . . .)$ +isin $\frac{π}{2}$ $(1 + \frac{1}{2} + \frac{1}{2^{2}} + . . . . . . .)$

= cos $\frac{π}{2}$ $(\frac{1}{1 - \frac{1}{2}})$ + isin $\frac{π}{2}$ $(\frac{1}{1 - \frac{1}{2}})$ = cos+isin $π$ = -1

Suggest Corrections

Similar questions

Q. Find the value of the expression

(c o s \frac{π}{2} + i s i n \frac{π}{2}) (c o s \frac{π}{2^{2}} + i s i n \frac{π}{2^{2}}) . . .

\infty

Q. Find the value of the expression:

(cos \frac{π}{2} + i sin \frac{π}{2}) (cos \frac{π}{2^{2}} + i sin \frac{π}{2^{2}}) \dots to \infty

Q. The value of

{(\frac{1 + c o s \frac{π}{2} - i s i n \frac{π}{2}}{1 + c o s \frac{π}{2} + i s i n \frac{π}{2}})}^{2}

Q. Find the value of

(c o s \frac{π}{8} + i s i n \frac{π}{8}) \times (c o s \frac{π}{12} + i s i n \frac{π}{12}) \times (c o s \frac{π}{24} + i s i n \frac{π}{24}) \times (c o s \frac{π}{4} + i s i n \frac{π}{4})

___

The polar form of $(i^{25})^{3}$ is

Join BYJU'S Learning Program

The value of Expression (cosπ2+isinπ2) (cosπ22+isinπ22)...........to ∞is

The correct option is A -1 (cosπ2+isinπ2)(cosπ22+isinπ22)...........to ∞ is = cos(π+π2+π22+.......) +isin(π+π2+π22+.......) =cosπ2(1+12+122+.......) +isinπ2(1+12+122+.......) = cosπ2(11−12) + isinπ2(11−12) = cos+isinπ= -1

The value of Expression $(c o s \frac{π}{2} + i s i n \frac{π}{2})$

$(c o s \frac{π}{2^{2}} + i s i n \frac{π}{2^{2}})$ ...........to $\infty$ is