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  • Help me answer: - Complex numbers and quadratic equations - JEE Main-5

If  a^{2}+i\left ( 5a-6 \right )= \left ( 3a-2 \right )+i\left ( a^{2} \right ) then 'a' equals \left ( Where\; a\, \epsilon \, R \right )

  • Option 1)

    1

  • Option 2)

    2

  • Option 3)

    3

  • Option 4)

    4

 

Answers (1)

Since, complex numbers are equal so 

a^{2}=3a-2\, \Rightarrow \, a^{2}-3a+2=0\, \Rightarrow \, a=1\: or\: 2

and 5a-6=a^{2}\, \Rightarrow \, a^{2}-5a+6=0\, \Rightarrow \, a=2\: or\: 3

Both real and imaginary parts should be equal corresponding & simultaneously which will be possible when a=2

\therefore Option (B)

 

Equality in Complex Numbers -

z=x+iy & w=a+ib are equal iff x=a & y=b

- wherein

Two complex numbers are equal iff real parts as well as imaginary parts are equal.

 

 


Option 1)

1

This is incorrect

Option 2)

2

This is correct

Option 3)

3

This is incorrect

Option 4)

4

This is incorrect

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