Question regarding complex numbers

In summary, the conversation discusses the relationship between a complex number, specifically a = cosα + i sinα, and the quadratic equation az2 + az +1 =0 with a purely imaginary root. The use of demoivre's theorem and the quadratic formula were attempted, but the correct solution was not reached until the clarification of the purely imaginary root was made.
  • #1
Mohsin Hussain
2
0
1)If a= cosα + i sinα and the equation az2 + az +1 =0 has a pure imaginary root, then tanα=?

2) cosα+isinα=e , quadratic formula

3) What i tried to do was,i put a constant real number and tried to solve it and used demoivres theorem, although the answer is getting weirder and weirder.
 
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  • #2
You need to show your work.
 
  • #3
PeroK said:
You need to show your work.
Yes, please show what you have done, Mohsin Hussain.

This is an important piece of information --
the equation az2 + az +1 =0 has a pure imaginary root
 
  • #4
sorry for bothering, it was a fairly easy one. didnt read the word "purely". Thanks.
 

Question 1: What are complex numbers?

Complex numbers are numbers that consist of a real part and an imaginary part. They are written in the form a + bi, where a is the real part and bi is the imaginary part (b is a real number and i is the imaginary unit, equal to the square root of -1).

Question 2: How are complex numbers represented on a graph?

Complex numbers are represented on a graph using the Cartesian coordinate system, with the real part being represented on the horizontal axis and the imaginary part on the vertical axis. The point where the two axes intersect is the origin, which represents the complex number 0 + 0i.

Question 3: What is the difference between real and imaginary numbers?

Real numbers are numbers that can be represented on the number line and include all rational and irrational numbers. Imaginary numbers, on the other hand, cannot be represented on the number line and are numbers that when squared, result in a negative number. They are used to represent the square root of negative numbers.

Question 4: What is the purpose of using complex numbers in mathematics?

Complex numbers are used in many areas of mathematics, including algebra, calculus, and trigonometry. They are particularly useful in solving equations that involve the square root of negative numbers, such as in electrical engineering and physics. They also have applications in signal processing, cryptography, and computer graphics.

Question 5: How do you perform operations with complex numbers?

To add or subtract complex numbers, you simply add or subtract the real parts and the imaginary parts separately. To multiply complex numbers, you use the FOIL method (multiply the First terms, the Outer terms, the Inner terms, and the Last terms) and combine like terms. To divide complex numbers, you use the conjugate of the denominator to eliminate the imaginary part and then simplify the resulting expression.

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