Question

Simplify (27+8i)/(3+2i^3)

Answer 1

Answer:

5 + 6i

Step-by-step explanation:

Need two things here:

• a³ - b³ = ( a - b ) ( a² + ab + b² )
• i³ = (i²)i = -i

Using these, we get:

( 27 + 8i ) / ( 3 + 2i³ )

= ( 27 - 8i³ ) / ( 3 - 2i )

= ( 3³ - (2i)³ ) / ( 3 - 2i )

= 3² + (3)(2i) + (2i)²

= 9 + 6i - 4

= 5 + 6i

Hope that helps.