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thatguythere
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Homework Statement
Use exponential notation to write (√3-i)(1+i√3) in the form a+ib.
Homework Equations
The Attempt at a Solution
Let (√3-i) = z1
r1=|z1|=√((√3)2-i2)
=√(3-1)
=√2
Therefore,
√3=√2cosθ and -1=√2sinθ
cosθ = √3/√2 and sinθ = -1/√2
θ= arcsin(-1/√2)
θ= -∏/4
z1 = √2(cos(-∏/4)+isin(-∏/4))
Let (1+i√3) = z2
r2 = |z2| = √(12+(i√3)2)
= √(1+(1(3)) <-- I am very uncertain about this step
= √4
= 2
Therefore
1 = 2cosθ and 3 = 2sinθ
cosθ = 1/2 and sinθ = 3/2
However,
θ=arcsin(3/2) does not compute which leads me to believe that (i√3)2 = 3 is incorrect. Any help is appreciated. Thank you.