123k views
3 votes
Please help me answer this question

Please help me answer this question-example-1

1 Answer

6 votes

Answer:

  • modulus: 3√2
  • argument: -3π/4 (or 5π/4)

Explanation:

The modulus is the magnitude of the complex number; the argument is its angle (usually in radians).

__

rectangular form

The complex number can be cleared from the denominator by multiplying numerator and denominator by its conjugate:


(-9+3i)/(1-2i)=((-9+3i)(1+2i))/((1-2i)(1+2i))=(-9+3i-18i-6)/(1+4)=-3-3i

polar form

The magnitude of this number is the root of the sum of the squares of the real and imaginary parts:

modulus = √((-3)² +(-3)²) = 3√2

The argument is the arctangent of the ratio of the imaginary part to the real part, taking quadrant into consideration.

arg = arctan(-3/-3) = -3π/4 or 5π/4 . . . . radians

__

modulus∠argument = (3√2)∠(-3π/4)

User Kavindra
by
8.3k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories