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If z = 1 - square root 3i, what is z^3 Answers -8 8 -8i 8i

If z = 1 - square root 3i, what is z^3 Answers -8 8 -8i 8i
196k views
12 votes
If z = 1 - square root 3i, what is z^3

Answers
-8
8
-8i
8i

User Krysta
by
8.3k points

2 Answers

13 votes

Answer:

A

Explanation:

Edge 2023

User Timbram
by
8.2k points
12 votes

Answer:


z = 1 - √(3) i \\ {z}^(3) = (1 - √(3) i) ^(3) \\ =(1 - √(3) i)(1 - √(3) i)(1 - √(3) i) \\ open \: brackets \\ = (1 - 2 √(3) i + ( { √(3) i})^(2) )(1 - √(3) i) \\ but \: {( √(3)i) }^(2) = - 3 \: since \: {i}^(2) \: is \: - 1 \: in \: complex \: numbers \\ = (1 - 2 √(3) i - 3)(1 - √(3) i) \\ = ( - 2 - 2 √(3) i)(1 - √(3) i) \\ = ( - 2 + 2 √(3) i - 2 √(3) i + 2( { √(3) i)}^(2) ) \\ = - 2 - 6 \\ = - 8

User Jonathan Joosten
by
8.0k points
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