Note that i is an imaginary number i.e i=√-1
Answers
Answer:
Required values of x are 0 and 3√2.
If x is a complex number, it is 2i.
Step-by-step explanation:
Given,
x^2 - ( 3√2 + 2i )x + 6√2i = 0
Case 1 : If x is a real number.
= > x^2 - 3√2x - 2xi + 6√2i = 0 + i( 0 ) { where i is the imaginary number and 0 is a real number }
= > ( x^2 - 3√2x ) + ( - 2xi + 6√2i ) = 0 + i(0)
= > ( x^2 - 3√2x ) + ( - 2x + 6√2 )i = 0 + i(0)
Comparing both sides :
= > - 2x + 6√2 = 0
= > 2x = 6√2
= > x = 3√2
Or,
= > x^2 - 3√2x = 0
= > x( x - 3√2 ) = 0
= > x = 0 or x = 3√2
Hence the required values of x are 0 and 3√2.
Case 2 : If x is a complex number.
= > x^2 - 3√2x - 2xi + 6√2i = 0
= > ( x^2 - 3√2x ) + ( - 2xi + 6√2i ) = 0
= > ( x^2 - 3√2x ) + ( - 2x + 6√2 )i = 0
= > x( x - 3√2 ) - 2i( x - 3√2 ) = 0
= > ( x - 3√2 )( x - 2i ) = 0
= > x = 3√2 or 2i
Thus, required complex value x is 2i.
Answer:
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