What is (5-3i+5i^5)-(-3+8i) ?

The solution to (5-3i+5i^5)-(-3+8i) is 8-6i

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simplify (5-3i+5i^5)-(-3+8i)

simplify

(5 - 3 i + 5 i^{5}) - (- 3 + 8 i)

8 - 6 i

Solution steps

(5 - 3 i + 5 i^{5}) - (- 3 + 8 i)

Apply rule:

(a) = a

(5 - 3 i + 5 i^{5}) = 5 - 3 i + 5 i^{5}

= 5 - 3 i + 5 i^{5} - (- 3 + 8 i)

i^{5} = i

- (- 3 + 8 i) = - (- 3) - 8 i

= 5 - 3 i + 5 i - (- 3) - 8 i

Apply rule:

a - (- b) = a + b

5 i - (- 3) = 5 i + 3

= 5 - 3 i + 5 i + 3 - 8 i

Group like terms

= - 3 i + 5 i - 8 i + 5 + 3

Add similar elements:

- 3 i + 5 i - 8 i = - 6 i

= - 6 i + 5 + 3

Add the numbers:

5 + 3 = 8

= - 6 i + 8

Rewrite in standard complex form:

8 - 6 i

= 8 - 6 i

\frac{4}{7} + \frac{3}{5}

(cos (2 t) + 2 t sin (2 t))^{2}

\frac{2 - 2}{3 + 2}

\frac{1}{cos ( x )} \cdot \frac{1}{cos ( x )}

sin^{3} (a) + sin (a) cos^{2} (a)