Express √3 + i in polar form:
|√3 + i| = √((√3)² + 1²) = √4 = 2
arg(√3 + i) = arctan(1/√3) = π/6
Then
√3 + i = 2 (cos(π/6) + i sin(π/6))
By DeMoivre's theorem,
(√3 + i)³ = (2 (cos(π/6) + i sin(π/6)))³
… = 2³ (cos(3 • π/6) + i sin(3 • π/6))
… = 8 (cos(π/2) + i sin(π/2))
… = 8i
Your mistake was in this part 9 x 1/100 . After the decimal point the place value starts with tenths so you should write 9 x 1/10 .
Place values
Before the decimal
point
3 ones = 3 x 1
0 tens = 0 x 10
1 hundreds = 1 x 100
After the decimal
point
9 tenths = 9 x 1/10
0 hundredths = 0 x 1/100
3 thousandths= 3 x 1/1000
1 x 100 + 0 x 10 + 3 x 1 + 9 x 1/10 + 0 x 1/100 + 3 x 1/1000
100 + 0 + 3 + 0.9 + 0 + 0.003
100 + 3 +
0.9 + 0.003 = 103.903
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0.3 times 100 = 30
300 thousands = 0.300.
No it does not
