1. Get more free challenging math and physics problems at briliant.org
You're done with this section! Check back next week to view solutions. Go back home
Details and assumptions
is the imaginary number satisfying .
KEY TECHNIQUES
De Moivre's Formula, Polar Coordinates, Complex Numbers, Trigonometric Functions
ANSWER
32
The complex number can be written as . What is the value of ?[2[cos( ) + i sin( )]]π
10
π
10
5
a + bi a + b
i = −1i2
From de Moivre's formula, we have
Thus, and . Hence, .
[2(cos( ) + i sin( ))]
π
10
π
10
5
= [cos( ) + i sin( )]25 5π
10
5π
10
= 32(cos( ) + i sin( ))
π
2
π
2
= 32(0 + i)
= 32i.
a = 0 b = 32 a + b = 0 + 32 = 32
Complex Representations
70 points
Brilliant
Page 1 of 1Complex Representations | Brilliant
6/13/2013https://brilliant.org/assessment/s/algebra-and-number-theory/2301963/
![Get more free challenging math and physics problems at briliant.org
You're done with this section! Check back next week to view solutions. Go back home
Details and assumptions
is the imaginary number satisfying .
KEY TECHNIQUES
De Moivre's Formula, Polar Coordinates, Complex Numbers, Trigonometric Functions
ANSWER
32
The complex number can be written as . What is the value of ?[2[cos( ) + i sin( )]]π
10
π
10
5
a + bi a + b
i = −1i2
From de Moivre's formula, we have
Thus, and . Hence, .
[2(cos( ) + i sin( ))]
π
10
π
10
5
= [cos( ) + i sin( )]25 5π
10
5π
10
= 32(cos( ) + i sin( ))
π
2
π
2
= 32(0 + i)
= 32i.
a = 0 b = 32 a + b = 0 + 32 = 32
Complex Representations
70 points
Brilliant
Page 1 of 1Complex Representations | Brilliant
6/13/2013https://brilliant.org/assessment/s/algebra-and-number-theory/2301963/](https://image.slidesharecdn.com/complexrepresentations-130619151454-phpapp02/85/complex-representations-1-320.jpg)
