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How can you rewrite the expression (8-5i)^2 in the form a+bi?
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How can you rewrite the expression (8-5i)^2 in the form a+bi?

User Liutas
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2 Answers

5 votes
(8 - 5i)²
(8 - 5i)(8 - 5i)
64 - 40i - 40i + 25i²
64 - 80i + 25i²
64 - 80i + 25(-1)
64 - 25 - 80i
39 - 80i
User Kviiri
by
8.6k points
2 votes
(a-b)^2 = a^2-2ab+b^2

(8-5i)^2 = 8^2-2(8)(5i)+(5i)^2

= 64-80i+25i^2

i^2=-1

So

= 64-80i+25(-1)

=64-25-80i

= 39 - 80i

which is your answer :)
User George Grover
by
8.5k points
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