If z-2 -3-2-i-25-2 -3-2-1-25- then

The correct option is B Im(z)=0 Given that z=(√(3)/2 +i 1/2)^5 + (√(3)/2 +i 1/2)^5 =[cosπ/6+isinπ/6]^5 + [cosπ/6 isinπ/6]^5 = cos5π/6+isin5π/6+cos5π/6 isin5π/6 ...

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Byju's Answer

Standard XI

Mathematics

Sign of Trigonometric Ratios in Different Quadrants

if z=2 √3/2+i...

Question

if z= ${(\frac{\sqrt[2]{3}}{2} + \frac{i}{2})}^{5}$ + ${(\frac{\sqrt[2]{3}}{2} - \frac{i}{2})}^{5}$ , then

Re(z)=0

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Im(z)=0

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Re(z)>0,Im(z)>0

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Re(z)>0,Im(z)<0

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Solution

The correct option is B
Im(z)=0

Given that z= ${(\frac{\sqrt[2]{3}}{2} + i \frac{1}{2})}^{5}$ + ${(\frac{\sqrt[2]{3}}{2} + i \frac{1}{2})}^{5}$

= ${[c o s \frac{π}{6} + i s i n \frac{π}{6}]}^{5}$ + ${[c o s \frac{π}{6} - i s i n \frac{π}{6}]}^{5}$

= cos $\frac{5 π}{6}$ +isin $\frac{5 π}{6}$ +cos $\frac{5 π}{6}$ -isin $\frac{5 π}{6}$

hence Im(z)=0

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Similar questions

Q. If

Z = {\frac{\sqrt{3}}{2} + \frac{i}{2}}^{5} + {\frac{\sqrt{3}}{2} - \frac{i}{2}}^{^{5}}

,then

Q. If

z = (\frac{\sqrt{3}}{2} + \frac{i}{2})^{5} + (\frac{\sqrt{3}}{2} - \frac{i}{2})^{5}

, then

Q. Let

z = {(\frac{\sqrt{3}}{2} + \frac{i}{2})}^{5} + {(\frac{\sqrt{3}}{2} - \frac{i}{2})}^{5}

. If

R (z)

and

I [z]

respectively denote the real and imaginary parts of

z

, then :

Q. State true or false:

z = {(\frac{\sqrt{3}}{2} + \frac{i}{2})}^{5} + {(\frac{\sqrt{3}}{2} - \frac{i}{2})}^{5}

, then

I m (z) = 0

Q. If

z = {(\frac{\sqrt{3}}{2} + i \frac{1}{2})}^{5} + {(\frac{\sqrt{3}}{2} - i \frac{1}{2})}^{5}

, then Im(z) =

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if z=(2√32+i2)5 + (2√32−i2)5 , then

The correct option is B Im(z)=0 Given that z=(2√32+i12)5 + (2√32+i12)5 =[cosπ6+isinπ6]5 + [cosπ6−isinπ6]5 = cos5π6+isin5π6+cos5π6-isin5π6 hence Im(z)=0

if z= ${(\frac{\sqrt[2]{3}}{2} + \frac{i}{2})}^{5}$ + ${(\frac{\sqrt[2]{3}}{2} - \frac{i}{2})}^{5}$ , then