calculus

posted by .

find the modulus and the argument of the following complex numbers:
15-4i and a-ai where a is greater than 0

  • calculus -

    if z = a + b i
    r^2 = sqrt( a^2 + b^2)
    and a = r cos T
    and b = r sin T

    so
    if a = 15
    and b = -4
    then r^2 = 15^2 + (-4)^2 = 225+16
    r = 15.524
    cos T = 15/15.524
    so T = 14.9 or -14.9
    sin T = -4/15.52
    so T = -14.9 or (180-14.9)=165.1
    T = -14.9 which is +345.1 in the fourth quadrant satisfies both, so that is it. (Besides we could see that 15-4i was in quadrant 4)

    r = sqrt (2 a^2) = a sqrt 2
    fourth quadrant again
    so
    sin T = -1/sqrt (2) = = -.707
    T = -45 degrees which is + 315 degrees

  • calculus -

    im sorry they were two different questions you have to find the modulus and the argument
    ex.15-4i
    modulus-4
    but i don't know what the argument is

  • calculus -

    I did them as two different questions
    for #1
    modulus = r = 15.524
    argument = T (for theta) = -14.9 degrees (or +345.1 degrees)

    for #2
    modulus = a sqrt 2
    theta = argument = -45 (or 315) degrees

  • calculus -

    thanks

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus--complex numbers

    the complex number Z satisfies Z/(Z+4)= 3+2i Find Z. please help thx!
  2. maths

    How do you convert degrees to radians? what's the modulus and the principle argument (complex n°)
  3. complex numbers

    how do you work out the the form a+ib when you are given the modulus and argument i.e. modulus=5,argument=pi/2
  4. ALGEBRA!!

    calculate P(i) for the following polynomial p(x)=x3+2x2-5x+8 Find | z | for each of the following complex numbers and represent them on a complex plane. a. z=-3-4i b. v=5-12i c.u=7+24i d.w=-9+40i e.p=1+3i f.t=-2i g.n=4 h.m=0 i.s=(√3-i)2
  5. TRIGONOMETRY

    Can someone please show me step by step how to calculate the modulus and the argument for these complex numbers?
  6. Pure Mathematics

    Find the modulus and principal argument of the complex numbers giving the argument in radians either as pi or a decimal correct to 2 decimal places c) i square root 3 -2 ALL UPON -2-i square root 3
  7. math-complex numbers

    Sketch the sets of complex numbers in the complex plane that satisfy the following: a) |z-1|=2 b) |z-3i|=2 c) |z-5+2i|=2 I'm not sure, but are you supposed to rearrange the whole thing to |z|=a+bi?
  8. Precalculus

    Let z and w be complex numbers such that |2z - w| = 25, |z + 2w| = 5, and |z + w| = 2. Find |z|. I need a little help with absolute values on complex numbers.
  9. Pre-cal

    The equation of the line joining the complex numbers -5 + 4i and 7 + 2i can be expressed in the form az + b*overline{z} = 38 for some complex numbers a and b. Find the product ab. Any help?
  10. Pre-calculus

    Let z and w be complex numbers such that |2z-2|=25, |z+2w|=5, and |z+w|=2. Find |z|. I first squared both equations and expressed the square of the magnitudes in terms of the complex numbers and its conjugates. Next, I summed the equations …

More Similar Questions