Simplify 3i+ 1/2 − 1/3 ( 1 − 3i ) + 2

(The answer is underlined)

3i + 1/2 - 1/3 (1-3i) + 2 = 13/6 + 4i

Steps

3i + 1/2 - 1/3 (1-3i) + 2

Multiply 1/3 (1-3i) :   1-3i/3

3i + 1/2 - 1-3i/3 + 2

Convert element to fraction:   3i = 3i/1, 2= 2/1

= 3i/1 + 1/2 - 1-3i/3 + 2/1

= 18i/6 + 3/6 - 1-3i • 2/6 + 12/6

Since the denominators are equal, combine the fractions:   a/c + b/c = a + b/c

= 18i + 3 - (1 - 3i) • 2 + 12:  13 + 24i/6

Expand 18i + 3 - (1 - 3i) • 2 + 12:  13 + 24i/6

13 + 24i/6

Rewrite 13 + 24i/6 in standard complex form: 13/6 + 4i

= 13/6 + 4i