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Find the complex number omega satisfying...

Find the complex number `omega` satisfying the equation `z^3=8i` and lying in the second quadrant on the complex plane.

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To find the complex number \( \omega \) satisfying the equation \( z^3 = 8i \) and lying in the second quadrant, we can follow these steps: ### Step 1: Rewrite the equation We start with the equation: \[ z^3 = 8i \] We can express \( 8i \) in polar form. The modulus of \( 8i \) is \( 8 \) and the argument (angle) is \( \frac{\pi}{2} \) (since it lies on the positive imaginary axis). ...
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CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
  1. If n is n odd integer that is greater than or equal to 3 but not a mul...

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  2. omega is an imaginary root of unity. Prove that If a+b+c = 0 th...

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  3. Find the complex number omega satisfying the equation z^3=8i and lying...

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  4. (1)/(a + omega) + (1)/(b+omega) +(1)/(c + omega) + (1)/(d + omega) =(1...

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  5. Write the following complex number in polar form : -3 sqrt(2) + ...

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  6. Let z(1)= cos 12^(@) + I sin 12^(@) and z(2) = cos 48^(@) + i. sin 4...

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  7. Covert the complex number z = 1 + cos (8pi)/(5) + i. sin (8pi)/(5) in ...

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  8. Let z and w be two nonzero complex numbers such that |z|=|w| and arg...

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  9. Find nonzero integral solutions of |1-i|^x=2^xdot

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  10. Let z be a complex number satisfying |z| = 3 |z-1|. Then prove that ...

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  11. If complex number z=x +iy satisfies the equation Re (z+1) = |z-1|, th...

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  12. Solve the equation |z|=z+1+2idot

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  13. Find the range of real number alpha for which the equation z+alpha|z-1...

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  14. Find the Area bounded by complex numbers arg|z|lepi/4 and |z-1|lt|z-3|

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  15. Prove that traingle by complex numbers z(1),z(2) and z(3) is equilate...

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  16. Show that e^(2m itheta)((icottheta+1)/(i cottheta-1))^m=1.

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

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

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

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  20. 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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