What is 1/3 i-(1/4-1/6 i) ?

The solution to 1/3 i-(1/4-1/6 i) is -1/4+1/2 i

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simplify 1/3 i-(1/4-1/6 i)

simplify

\frac{1}{3} i - (\frac{1}{4} - \frac{1}{6} i)

- \frac{1}{4} + \frac{1}{2} i

Solution steps

\frac{1}{3} i - (\frac{1}{4} - \frac{1}{6} i)

Remove parentheses:

- (a + bi) = - a - bi

= \frac{1}{3} i + - \frac{1}{4} - (- \frac{1}{6}) i

Apply rule:

- (- a) = a

- (- \frac{1}{6}) = \frac{1}{6}

= \frac{1}{3} i - \frac{1}{4} + \frac{1}{6} i

Factor out common term

i

= i (\frac{1}{3} + \frac{1}{6}) - \frac{1}{4}

\frac{1}{3} + \frac{1}{6} = \frac{1}{2}

= i \frac{1}{2} - \frac{1}{4}

= \frac{1}{2} i - \frac{1}{4}

Rewrite in standard complex form:

- \frac{1}{4} + \frac{1}{2} i

= - \frac{1}{4} + \frac{1}{2} i

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