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I'm really struggling with this, please help. 

 May 28, 2022
 #1
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3√6cis(π/8) and 2√5cis(7π/6)

 

assuming only the 5 sand 5 are under the square root

 

\([3\sqrt6 cis(π/8) ]*[ 2\sqrt5 cis(7π/6)]\\ =6\sqrt{30}*cis(π/8) ]* cis(7π/6)]\\ =6\sqrt{30}*cis(π/8) ]* cis(7π/6)]\\ =6\sqrt{30}*e^{(\pi/8)i}*e^{(7\pi/6)i}\\ =6\sqrt{30}*e^{((1/8)+(7/6))\pi i}\\ =6\sqrt{30}*e^{((3/24)+(28/24))\pi i}\\ =6\sqrt{30}*e^{(31/24)\pi i}\\ =6\sqrt{30}*cis{(31\pi/24)}\\ \)

 

I have not checked it.  That is your job

 

LaTex

[3\sqrt6 cis(π/8) ]*[ 2\sqrt5 cis(7π/6)]\\
=6\sqrt{30}*cis(π/8) ]* cis(7π/6)]\\
=6\sqrt{30}*cis(π/8) ]* cis(7π/6)]\\
=6\sqrt{30}*e^{(\pi/8)i}*e^{(7\pi/6)i}\\
=6\sqrt{30}*e^{((1/8)+(7/6))\pi i}\\
=6\sqrt{30}*e^{((3/24)+(28/24))\pi i}\\
=6\sqrt{30}*e^{(31/24)\pi i}\\
=6\sqrt{30}*cis{(31\pi/24)}\\

 May 29, 2022

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