MHT CET202123 Sep 2021Morning ShiftMathematicsComplex NumberActual
The square roots of the complex number (-5-12 i ) are
Options
- A(2-3 i)
- B(3+2 i )
- C(2+3 i)
- D(3-2 i )
Correct answer
A. (2-3 i)
Step-by-step solution
aligned & Let -5-12 i =a+i b [a, b R] & (a+i b)^2=-5-12 i & (a^2-b^2 )+i(2 a b)=-5-i(12) & a^2-b^2=-5 and 2 a b=-12 a b=-6 b= -6 a & a^2- ( -6 a )^2=-5 & a^4-36=-5 a^2 a^4+5 a^2-36=0 & (a^2+9 ) (a^2-4 )=0 a^2=4 [a R] & a= 2 b= -6 2 = 3 & -5-12 i = (2-3 i) aligned