Question

What is the trigonometric form of `(5+10i)(3+3i)`?

Answer 1

`15 \sqrt{10} text{ cis} ( text{Arc}text{tan}(-3) )`

Explanation:

`(5+10i)(3+3i) = 15(1+2i)(1+i) = 15(-1 + 3i)`

`= 15 \sqrt{1^2+3^2} (text{cis} ( arctan2(3 //, -1) ) }`

I employ the funny notation because it take a two parameter, four quadrant arctangent in general. This one's in the fourth quadrant, so the principal value of the arctangent is sufficient:

`= 15 \sqrt{10} text{ cis} ( text{Arc}text{tan}(-3) )`