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Let z(1)= cos 12^(@) + I sin 12^(@) and ...

Let `z_(1)= cos 12^(@) + I sin 12^(@) and z_(2) = cos 48^(@) + i. sin 48^(@)`. Write complex number `(z_(1) + z_(2))` in polar form. Find its modulus and argument.

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To solve the problem, we need to find the sum of the complex numbers \( z_1 \) and \( z_2 \), express it in polar form, and then find its modulus and argument. ### Step 1: Write down the complex numbers Given: \[ z_1 = \cos 12^\circ + i \sin 12^\circ \] \[ ...
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CENGAGE ENGLISH-COMPLEX NUMBERS-ILLUSTRATION
  1. (1)/(a + omega) + (1)/(b+omega) +(1)/(c + omega) + (1)/(d + omega) =(1...

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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