Question

simplify and expand (-1+√3i/2)^3​

Answer 1

Solution:

( -1 + √3i/2 )³

According to the identity

(a + b)³ = a³ + b³ + 3a²b + 3ab²

=> -1 + 3√3i³/8 + 3√3i/2 - 9i²/4

=> -1 - 3√3i/8 + 3√3i/2 - 9i²/4

=> -1 + 9/4 - ( 3√3i - 12√3i )/8

=> (-4+9)/4 - ( -9√3i)/8

=> 5/4 + 9√3i/8

Here,

Real part is 5/4 and imaginary part is 9√3i/8.

_____________________________

Extra information:

• i² = -1

• i³ = -i

• i⁴ = 1

Identities:

• (a - b)³ = a³ - 3a²b + 3ab² - b³

• a³ + b³ = (a + b)³ - 3ab (a + b)

• a³ - b³ = (a - b)³ + 3ab (a+b)

Answer 2

Step-by-step explanation:

( -1+√3i)³÷2

°-1³+3(-1)²(√3i)+3(-1)(√3i)²+(√3i)³÷2............=(a³+3a²b+3ab²+b³) formula of (a+b)³

=1+3√3i-3×3i²+3√3i÷2

=1+3√3-9i²+3√3i÷2..........(i²=-1)formula

=1+3√3-9(-1)+3√3÷2

=1+3√3-9-3√3÷2.......(+or- )

=1+-9÷2

=8÷2

=4