The expression 62/(3-i) can be written in standard form as:
(186 + 62i)/10
To write the expression 62/(3-i) as a complex number in standard form, we need to rationalize the denominator. Rationalizing the denominator means getting rid of any radicals or imaginary numbers in the denominator.
To rationalize the denominator in this case, we multiply the numerator and denominator by the conjugate of the denominator. The conjugate of 3-i is 3+i. Multiplying the numerator and denominator by 3+i gives us:
(62/(3-i)) * (3+i)/(3+i)
Now, let's simplify the expression:
62 * (3+i) = 186 + 62i
(3-i) * (3+i) = 3^2 - i^2 = 9 - (-1) = 9 + 1 = 10
Therefore, the expression 62/(3-i) can be written in standard form as:
(186 + 62i)/10
This is a complex number in standard form, where the real part is 186/10 and the imaginary part is 62/10i.
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