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Mathematics 59 Online

snowflake0531:

@AZ

4 years ago

snowflake0531:

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4 years ago

snowflake0531:

ig the first step would be to make it \(-7776i(cos(5\theta)+isin(5\theta)\) and then idk

4 years ago

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 \[z=0+(-6 \iota)\]

4 years ago

snowflake0531:

thank youuuuuuu!

4 years ago

surjithayer:

4 years ago

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