Modulus Argument form!

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Let z1= r(cosπ/4 + isinπ/4) and z2= 1+√3i. Write z2 in modulus argument form.

Bonus question (not part of the answer): For those who are smarter or more BRILLIANT, find the value of r if modulus(z1 X z2^3) =2. Post the answer for this bonus question as part of your comment below!

Assumptions: For z1, the term "i" in "isinπ/4" refers to the imaginary number i. For z2, the term "i" is outside the squareroot but is multiplied to √3, so √3i = i√3.

Note: Since Brilliant only allows answers to be in numbers for math problems, let option 1 be 2[cos π/3+isin π/3], option 2 be 4[cos π/4+isin π/4], option 3 be 2[cos π/4+isin π/4], option 4 be 4[cos π/6+isin π/6].


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