Modulus Argument form!
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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Let z2= 1+sqrt3 i.
Angle Theta = tan-1 (sqrt3) = pi/3 rad.
Therefore, arg z = pi/3 rad.
r = modulus(z) = sqrt (1^2+(sqrt3)^2) = 2.
Therefore, z2 = 2(cos pi/3 + isin pi/3).
Therefore, option 1 is the answer.
P.s. Lazy to do the bonus question and I am not smart enough. Others please advise on how to do the bonus question!