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snowflake0531:
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snowflake0531:
ig the first step would be to make it \(-7776i(cos(5\theta)+isin(5\theta)\) and then idk
surjithayer:
@surjithayer wrote:
\[\ z=r(\cos \theta+\iota \sin \theta)(say)\]
\[z^5=r^5(\cos \theta+\iota \sin \theta)^5=r^5(\cos 5\theta+\iota \sin 5\theta)=-7776 \iota \]
\[r^5=7776=6^5,r=6\]
\[\cos 5\theta=0,\sin 5\theta=-1,\]
so 5 \theta lies on y-axis.
as sin 5 \theta is negative ,so it is in 3rd or 4th quadrant.
\[5\theta =270=270+360n\]
where n is an integer.
\[\theta=54+72n\]
if n=1,\[\theta=54+72=126\]
n=2
\[\theta=54+144=198\]
n=3
\[\theta=54+216=270\]
n=4
\[\theta=54+288=362\]
so \[\theta=270\]
\[z=6(\cos 270+\iota \sin 270)\]
or
\[z=0+(-6 \iota)\]
snowflake0531:
thank youuuuuuu!
surjithayer:
yw
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