What is simplify-((9i)/2+3/14)+((-5i)/7-3) ?

The solution to simplify-((9i)/2+3/14)+((-5i)/7-3) is -45/14-73/14 i

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simplify-((9i)/2+3/14)+((-5i)/7-3)

simplify

- (\frac{9 i}{2} + \frac{3}{14}) + (\frac{- 5 i}{7} - 3)

- \frac{45}{14} - \frac{73}{14} i

Solution steps

- (\frac{9 i}{2} + \frac{3}{14}) + (\frac{- 5 i}{7} - 3)

Rewrite

\frac{9 i}{2} + \frac{3}{14}

in standard complex form:

\frac{3}{14} + \frac{9}{2} i

Rewrite

\frac{- 5 i}{7} - 3

in standard complex form:

- 3 + \frac{- 5}{7} i

= - (\frac{3}{14} + \frac{9}{2} i) + - 3 + \frac{- 5}{7} i

Apply factoring rule:

- a - b = - (a + b)

- (\frac{3}{14} + \frac{9}{2} i) + - 3 + \frac{- 5}{7} i = - (\frac{3}{14} + \frac{9}{2} i - (- 3 + \frac{- 5}{7} i))

= - (\frac{3}{14} + \frac{9}{2} i - (- 3 + \frac{- 5}{7} i))

Group the real part and the imaginary part of the complex number

(a + bi) - (c + d i) = (a - c) + (b - d) i

= - ((\frac{3}{14} - (- 3)) + (\frac{9}{2} - \frac{- 5}{7}) i)

Apply the distributive law:

- (a + b) = - a - b

- ((\frac{3}{14} - (- 3)) + (\frac{9}{2} - \frac{- 5}{7}) i) = - (\frac{3}{14} - (- 3)) - (\frac{9}{2} - \frac{- 5}{7}) i

= - (\frac{3}{14} - (- 3)) - (\frac{9}{2} - \frac{- 5}{7}) i

Simplify

- (\frac{3}{14} - (- 3)) - (\frac{9}{2} - \frac{- 5}{7}) i : - \frac{45}{14} - \frac{73}{14} i

= - \frac{45}{14} - \frac{73}{14} i

\frac{3}{4} x^{2} - 3 = - \frac{3}{4} x^{2} + 3

5 < \frac{1}{2} p + 3 < 8

2 lo g_{4} (9) - lo g_{2} (3)

∣ 5 x + 2 ∣ \geq 7

64 a^{3} + 1

What is simplify-((9i)/2+3/14)+((-5i)/7-3) ?
The solution to simplify-((9i)/2+3/14)+((-5i)/7-3) is -45/14-73/14 i