Solutions, cont'd (3)

(3) We have:

[z₃·z₄] = (z₃·z₄) cis(arg(z₃) – arg(z₄))

We already know: arg(z₃) = 14 deg.

And: z₃= 4.1 cis(14)

We also saw: z₄ = 4 + 3i = 5 cis (36.8)

And: arg(z₄) =  36.8  deg

Then write out the product, viz.:


[z₃•z₄] = (z₃•z₄) cis([arg(z₃) – arg(z₄)] =


[4.1][ 5] cis [arg (14 deg) – arg(36.8 deg)]


For which:


arg(z₃) – arg(z₄) = [(14) – (36.8)] = -22.8


Therefore:

[z₃•z₄] = 20.5 cis (-22.8) = = 20.5 [(cos (-22.8) + isin(-22.8)]


[z₃•z₄] = 20.5 [(0.92) + i(-0.38)]  = 18.9 - 7.8i   (rounded off )


(Note: The result above corrected from yesterday, since the angular difference in the arguments is (-22.8) not (-24.8)!)