In the following exercise, use the given complex numbers Z and W

label Mathematics
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Use the given complex #'s Z and W.
Z=4+5i and W=3i

And find and simplify the following.

a. Z+W

b. ZW


d. 1/Z (1 over Z)

e. Z/W (Z over W)

f. W/Z (W over Z)

Oct 1st, 2015

Thank you for the opportunity to help you with your question!

z+w = 4+8i

zw=(4+5i)*3i=12i-15 = -15+12i

z^2=(4+5i)^2=16+40i -25=-9+40i [using (a+b)^2 formula]

1/z=1/(4+5i)=(4-5i)/(4+5i)(4-5i)=4-5i/(16+25)=(4-5i)/41=4/41-(5/41)i  [multiply numerator and denominator by conjugate of numerator)

z/w=(4+5i)/(3i) = 4/(3i)+ 5/3=4*(-i)/(3i)*(-i)+5/3=5/3-4i/3 [multiply numerator and denominator by -i]

w/z=3i*(1/z)=3i*(4/41-(5/41)i)=(12/41)i+15/41=15/41+12i/41 (using earlier result already obtained of 1/z]

Please let me know if you need any clarification. I'm always happy to answer your questions.
Oct 1st, 2015

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