Write 1-2i in Polar Form - Solve Confusion

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SUMMARY

The polar form of the complex number 1-2i is determined by calculating the modulus and argument. The modulus, r, is √5, while the argument can be derived using the arctangent function. The correct angle is 296.57°, as the complex number lies in the fourth quadrant, where the real part is positive and the imaginary part is negative. The confusion arises from the use of the sine inverse, which can yield an incorrect angle without proper quadrant consideration.

PREREQUISITES
  • Understanding of complex numbers and their representation
  • Knowledge of polar coordinates and conversion from rectangular form
  • Familiarity with trigonometric functions, specifically sine and arctangent
  • Ability to determine quadrants based on the signs of real and imaginary parts
NEXT STEPS
  • Study the conversion of complex numbers to polar form in detail
  • Learn about the properties of the arctangent function and its limitations
  • Explore the significance of quadrants in complex number analysis
  • Practice additional examples of converting complex numbers to polar form
USEFUL FOR

Students studying complex numbers, mathematics enthusiasts, and anyone seeking to improve their understanding of polar coordinates and trigonometric functions in relation to complex analysis.

dylanhouse
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Homework Statement



How do I write 1-2i in polar form?

Homework Equations





The Attempt at a Solution



I know r=√5, and when using x=rcosθ, I get angle of 63.43 or 296.57. However, when I take the sin inverse of-2/√5 I get -63.43. I am really confused.
 
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dylanhouse said:

Homework Statement



How do I write 1-2i in polar form?

Homework Equations





The Attempt at a Solution



I know r=√5, and when using x=rcosθ, I get angle of 63.43 or 296.57. However, when I take the sin inverse of-2/√5 I get -63.43. I am really confused.
The angle is in the 4th quadrant, so it would be either -63.43° or +296.57° (assuming your figures are correct.
 
dylanhouse said:

Homework Statement



How do I write 1-2i in polar form?

Homework Equations





The Attempt at a Solution



I know r=√5, and when using x=rcosθ, I get angle of 63.43 or 296.57. However, when I take the sin inverse of-2/√5 I get -63.43. I am really confused.

The formula is arc tan (Im part)/(Real part). You need to keep track of the numerator and denominator signs to make sure you land in the correct quadrant. In other words, the fact that the I am is - and the Re is + tells you which quadrant to land in.
 

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