The complex solutions of which equation have a real component of 4 is x² - 8x +16 +21 = 0.
What is Complex number?
Complex numbers are numbers that consist of two parts — a real number and an imaginary number.
On solving all equation the correct one is x² - 8x +16 = -21.
Using discriminant method calculating the roots
x² - 8x +16 +21 = 0
x² - 8x + 37 = 0
x= -b ± √b² -4ac / 2a
x= 8 ± √ -8² - 4*1 * (37) /2a
x= 8 ± √- 84 / 2
x= 8 ± √2² *(- 21) /2
x=( 8 ± √2² *√21 i)/2
x= 8 / 2 ± 2i√21/2
x= 4 ± √21 i
So, x = 4+ √21 i and x= 4 - √21 i
Learn more about complex numbers here:
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