x=(21.83+60.66i)/(-5.15-5.89i)

i is the square root of (-1)
then x should equal 10.3
but i do not know how to figure it out
please show me
thank you

To compute the value of x, we can use the concept of division involving complex numbers. To perform this calculation, we need to rationalize the denominator, which involves multiplying both the numerator and denominator by the conjugate of the denominator.

The conjugate of a complex number a + bi is obtained by changing the sign of the imaginary part. In this case, the conjugate of -5.15 - 5.89i is -5.15 + 5.89i.

Step 1: Multiply the numerator and denominator by the conjugate of the denominator:
x = ((21.83 + 60.66i) * (-5.15 + 5.89i)) / ((-5.15 - 5.89i) * (-5.15 + 5.89i))

Step 2: Perform the multiplication in the numerator and denominator:
x = (-112.3245 + 203.2054i) / (26.5125 + 28.6755i^2)

Step 3: Simplify the denominator:
Since i is defined as the square root of -1, i^2 = -1. Therefore, we can substitute i^2 with -1.
x = (-112.3245 + 203.2054i) / (26.5125 + 28.6755(-1))

Step 4: Simplify further:
x = (-112.3245 + 203.2054i) / (26.5125 - 28.6755)

Step 5: Calculate the numerator and denominator:
x = (-112.3245 + 203.2054i) / (-2.163)

Step 6: Divide the numerator by the denominator:
x ≈ (-112.3245 / -2.163) + (203.2054i / -2.163)

Step 7: Calculate the real and imaginary parts separately:
x ≈ 51.9390 - 94.0520i

So the value of x is approximately 51.9390 - 94.0520i. It seems that the value of x you mentioned (10.3) is not correct.