The easiest way, I think, is to convert the mixed number into an improper fraction, then multiply by 3.
3 1/2 = 7/2
7/2 · 3 = 21/2
now just change the improper fraction back to a mixed number by dividing and putting the remainder into fraction form
21/2 = 10 1/2
You could also multiply the whole number by 3 and the fraction by 3, ending up with 9 3/2, but then have to convert the improper fraction into a mixed number
3/2 = 1 1/2
then add the numbers together
9 + 1 1/2 = 10 1/2
either way works, whatever is easiest for you.
The conversion factor should be multiplied in Step 2 instead of being divided.
The given complex number is
z = 1 + cos(2θ) + i sin(2θ), for -1/2π < θ < 1/2π
Part (i)
Let V = the modulus of z.
Then
V² = [1 + cos(2θ)]² + sin²(2θ)
= 1 + 2 cos(2θ) + cos²2θ + sin²2θ
Because sin²x + cos²x = 1, therefore
V² = 2(1 + cos2θ)
Because cos(2x) = 2 cos²x - 1, therefore
V² = 2(1 + 2cos²θ - 1) = 4 cos²θ
Because -1/2π < θ < 1/2π,
V = 2 cosθ PROVEN
Part ii.
1/z = 1/[1 + cos2θ + i sin 2θ]

The denominator is

Therefore

The real part of 1/ = 1/ (constant).
LIST has 5 lines: L has two, I has 1, T as 2. It has one curve: S.
Therefore LIST = 51
LOAD has 6 lines, 2 curves.
L has 2 lines, A has 3 lines, D has one line (also one curve)
O is one curve, D has one, so LOAD= 62
Given:
discount of 25%
Hasan's equation: d - 0.25d
Bella's equation: 0.75d
d represents the original price.
0.25d represents the discount.
0.75d represents the discounted price.
Example: 1,000 is the price. d = 1,000
0.25d = 0.25(1000) = 250 this is the discount
0.75d = 0.75(1000) = 750 this is the discounted price
Hassan: d - 0.25d = 1000 - 250 = 750
Bella: 0.75d = 0.75(1000) = 750