Write [2 (cos15+isin15) ]^3 in standard form a+bi

Question

Mathematics

Chamberlain

16 August, 16:47

Write [2 (cos15+isin15) ]^3 in standard form a+bi

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Elsie Rivers · Answer 1

Hello:

by moivre theorem:

[2 (cos15*+isin15*) ]^3 = 2^3 (cos (3*45*) + isin (3*45*))

=8 (cos45*+isin45*)

= 8 (√2/2 + i √2/2)

= 4√2 + 4√2 i ... (in standard form a+bi)

a = b = 4√2

Write [2 (cos15*+isin15*) ]^3 in standard form a+bi

Write [2 (cos15+isin15) ]^3 in standard form a+bi