The imaginary part of conjugate of 1 - i1 - i 5 is

The correct option is A 1 1+i1 i = (1+i)^22 =1+i^2+2i2 =i ( i^2 = 1 ) (1+i1 i) ^5 =i^5 =i conjugate of this is = i imaginary part ...

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Standard XII

Mathematics

Conjugate of a Complex Number

The imaginary...

Question

The imaginary part of conjugate of ${(\frac{1 + i}{1 - i})}^{5}$ is

- 1

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Solution

The correct option is A $- 1$
$\frac{1 + i}{1 - i} = \frac{(1 + i)^{2}}{2} = \frac{1 + i^{2} + 2 i}{2} = i$ ( $i^{2} = - 1$ )

$(\frac{1 + i}{1 - i})^{5} = i^{5} = i$

conjugate of this is $= - i$

imaginary part $= - 1$

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The imaginary part of conjugate of (1+i1−i)5 is

The correct option is A −11+i1−i=(1+i)22=1+i2+2i2=i (i2=−1)(1+i1−i)5=i5=iconjugate of this is =−iimaginary part =−1

The imaginary part of conjugate of ${(\frac{1 + i}{1 - i})}^{5}$ is

The correct option is A $- 1$
$\frac{1 + i}{1 - i} = \frac{(1 + i)^{2}}{2} = \frac{1 + i^{2} + 2 i}{2} = i$ ( $i^{2} = - 1$ )

$(\frac{1 + i}{1 - i})^{5} = i^{5} = i$

conjugate of this is $= - i$

imaginary part $= - 1$