SOLUTION: (3/2+1/3i)+(1/6-3/4i)

Question 345342: (3/2+1/3i)+(1/6-3/4i)
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
((3)/(2)+(1)/(3)*i)+((1)/(6)-(3)/(4)*i)
Multiply (1)/(3) by i to get (i)/(3).
((3)/(2)+(i)/(3))+((1)/(6)-(3)/(4)*i)
Multiply -(3)/(4) by i to get -(3i)/(4).
((3)/(2)+(i)/(3))+((1)/(6)-(3i)/(4))
Remove the parentheses that are not needed from the expression.
(3)/(2)+(i)/(3)+(1)/(6)-(3i)/(4)
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 6. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(1)/(6)+(3)/(2)*(3)/(3)+(i)/(3)-(3i)/(4)
Complete the multiplication to produce a denominator of 6 in each expression.
(1)/(6)+(9)/(6)+(i)/(3)-(3i)/(4)
Combine the numerators of all fractions that have common denominators.
(1+9)/(6)+(i)/(3)-(3i)/(4)
Add 9 to 1 to get 10.
(10)/(6)+(i)/(3)-(3i)/(4)
Reduce the expression (10)/(6) by removing a factor of 2 from the numerator and denominator.
(5)/(3)+(i)/(3)-(3i)/(4)
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 12. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
(5)/(3)-(3i)/(4)*(3)/(3)+(i)/(3)*(4)/(4)
Complete the multiplication to produce a denominator of 12 in each expression.
(5)/(3)-(9i)/(12)+(4i)/(12)
Combine the numerators of all expressions that have common denominators.
(5)/(3)+(-9i+4i)/(12)
Combine all like terms in the numerator.
(5)/(3)+(-5i)/(12)
Move the minus sign from the numerator to the front of the expression.
(5)/(3)-(5i)/(12)
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