If x r -cos-3 r - isin -3 r - then x 1 x 2 x 3- - to - is-A- -1B- -iC- 1D- i

The correct option is D i (cosα + i sinα) (cosβ + i sinβ) = cos(α + β) + i sin(α + β) x_1 x_2 x_3...... = cis (π/3( 1/1 1/3)) = cisπ/2 = i ...

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Polar Representation of a Complex Number

If x r =cosπ/...

Question

If $x_{r} = c o s (\frac{π}{3^{r}}) + i s i n (\frac{π}{3^{r}})$ , then $x_{1} x_{2} x_{3} . . . . . . . t o \infty i s$ :

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-i

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Solution

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Similar questions

x_{r} = cos (\frac{π}{3^{r}}) + i sin (\frac{π}{3^{r}})

x_{1} \cdot x_{2} \cdot x_{3} . . . \infty

A_{r} = cos \frac{π}{3^{r}} + i sin \frac{π}{3^{r}},

A_{1} \cdot A_{2} \cdot A_{3} \cdot \dots \cdot A_{\infty}

i = \sqrt{- 1}

X_{r} = cos \frac{π}{2^{r}} + i sin \frac{π}{2^{r}}

X_{1} X_{2} X_{3} . . . . \infty

z_{r} = cos (\frac{π}{3^{r}}) + i sin (\frac{π}{3^{r}}), r = 1, 2, 3, . . .

z_{1} . z_{2} . z_{3} . . . \infty =

A_{r} = cos \frac{π}{3^{r}} + i sin \frac{π}{3^{r}},

A_{1} \cdot A_{2} \cdot A_{3} \cdot \dots \cdot A_{\infty}

i = \sqrt{- 1}

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