Need help with complex numbers questions:
−14+12i has argument: θ=
7−15i has argument: θ=
−10−13i has argument: θ=
for any complex number of the form a + bi
your angle θ is found from tanθ = b/a
I will do the 2nd one, you do the other two.
tanθ = -15/7
you know 7−15i is in quadrant IV of the Argand plane, so
find tan^-1 (+15/7), which is 1.134169... radians
so in quad IV, θ = 2π - 1.134169 = 5.149016...
If you want it in degrees, make sure your calculator is set to DEG using the DRG key
I got appr 295.017°
To find the argument (or angle) of a complex number in rectangular form, you can use the formula:
θ = arctan(b/a)
where "a" represents the real part of the complex number and "b" represents the imaginary part.
Let's calculate the arguments of the given complex numbers step by step:
1. For −14+12i:
- a = -14 (real part)
- b = 12 (imaginary part)
- θ = arctan(12 / -14)
- Using a calculator or math software, find the value of arctan(12 / -14) ≈ -41.19 degrees.
Therefore, the argument of −14+12i is θ ≈ -41.19 degrees.
2. For 7−15i:
- a = 7 (real part)
- b = -15 (imaginary part)
- θ = arctan(-15 / 7)
- Using a calculator or math software, find the value of arctan(-15 / 7) ≈ -64.22 degrees.
Therefore, the argument of 7−15i is θ ≈ -64.22 degrees.
3. For −10−13i:
- a = -10 (real part)
- b = -13 (imaginary part)
- θ = arctan(-13 / -10)
- Using a calculator or math software, find the value of arctan(-13 / -10) ≈ 48.37 degrees.
Therefore, the argument of −10−13i is θ ≈ 48.37 degrees.
Remember that the argument can also be given in radians, depending on the context.