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Find the real part of (1-i)^(-i)dot...

Find the real part of `(1-i)^(-i)dot`

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To find the real part of \((1-i)^{-i}\), we can follow these steps: ### Step 1: Rewrite the expression Let \( z = (1-i)^{-i} \). ### Step 2: Take the logarithm Taking the natural logarithm on both sides, we have: \[ ...
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CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
  1. Show that e^(2m itheta)((icottheta+1)/(i cottheta-1))^m=1.

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  2. Z1!=Z2 are two points in an Argand plane. If a|Z1|=b|Z2|, then prove t...

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  3. Find the real part of (1-i)^(-i)dot

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  4. If (sqrt(8)+i)^(50)=3^(49)(a+i b) , then find the value of a^2+b^2dot

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  5. Show that (x^2+y^2)^4=(x^4-6x^2y^2+y^4)^2+(4x^3y-4x y^3)^2dot

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  6. If a rg(z1)=170^0a n d arg(z2)70^0 , then find the principal argument ...

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  7. Find the value of expression (cos(pi/2)+isin(pi/2))(cos(pi/(2^2))+isin...

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  8. Find the principal argument of the complex number ((1+i)^5(1+sqrt(3i))...

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  9. If z=((sqrt(3)+i)^(17))/((1-i)^(50)) , then find a m p(z)dot

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  10. If z=x+i y and w=(1-i z)/(z-i) , show that |w|=1 z is purely real.

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  11. It is given the complex numbers z(1) and z(2), |z(1)| =2 and |z(2)| ...

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  12. Solve the equation z^(3) = barz (z ne 0)

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  13. If 2z1//3z2 is a purely imaginary number, then find the value of "|"(z...

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  14. Find the complex number satisfying the system of equations z^3+ omega^...

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  15. Express the following in a + ib form: (i) ((cos theta+ isin theta...

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  16. Let z = ((sqrt(3))/(2) + (i)/(2))^(5)+((sqrt(3))/(2)-(i)/(2))^(5). If ...

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  17. Prove that the roots of the equation x^4-2x^2+4=0 forms a rectangle.

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  18. If z + 1/z = 2costheta, prove that |(z^(2n)-1)//(z^(2n)+1)|=|tannthet...

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  19. If z=x+i y is a complex number with x ,y in Qa n d|z|=1, then show th...

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  20. If z=costheta+isintheta is a root of the equation a0z^n+a2z^(n-2)+.......

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