Question #252555

A complex number z satisfies the equation z2=3+4i.z^{2}=3+4i.

Which of the following is true about zz ?




  1. (3+4i)2=25+24i(3+4i)^{2}=25+24i
  2. z=±(2+i)z=\pm (2+i)
  3. (3+4i)2=9+40i(3+4i)^{2}=9+40i
  4. z=±(2+2i)z=\pm (2+2i)
  5. (3+4i)2=7+24i(3+4i)^{2}=-7+ 24i
1
Expert's answer
2021-10-19T16:10:02-0400

Z2=3+4i,Z2-3-4i=0,


using quadratic formula,


Z=(−b±√(b2 − 4ac))/2a


where a=1,b=0,c=(-3-4i)


Z=(-0±√(02-4x1x(-3-4i)))/(2x1)


Z=(0±√(12+16i))/2


Z=(±(4+2i))/2


Z=±(2+i). Hence 2 is correct.




(3+4i)2=(3+4i)(3+4i)


(3+4i)2=9+12i+12i+(4i)2

(3+4i)2=9+24i+16(√(-1))2

(3+4i)2=9+24i+16(-1)


(3+4i)2=9+24i-16


(3+4i)2=(9-16)+24i


(3+4i)2=-7+24i.


Hence 5 is correct.


Therefore 2 and 5 are correct


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