Find the point on the line y = 2x +1 that is closest to the point (5, 2).
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Multiply both numerator and denominator of by the complex conjugate of the denominator, -2+9i.
Multiplication can be transformed into difference of squares using the rule: .
By definition, i² is -1. Calculate the denominator.
Multiply complex numbers 5-3i and -2+9i in the same way as you multiply binomials.
Do the multiplications in .
Combine the real and imaginary parts in -10+45i+6i+27.
Do the additions in .
Divide 17+51i by 85 to get .
The real part of is
.
Let's assume they meant C=40 degrees. With an angle like that they're asking for approximation; we'll oblige.
The circumradius is the product of the triangle sides divided by four times the area.
Here we have remaining side given by the Law of Cosines.
The area is
The circumradius is
The circumradius is the product of the triangle sides divided by four times the area.
Here we have remaining side given by the Law of Cosines.
The area is
The circumradius is