Angle and absolute value of complex numbers

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  1. Given the complex number z=2+3iz=2+3i
    1. Find its absolute value
    2. Find the angle it makes in the complex plane in radians
  2. Given the complex number w=5i3 w=5i-3
    1. Find its modulus
    2. Find its argument in radians
  3. Given that a complex number ww makes an angle θ=3π4\theta=\frac{3\pi}{4} in the complex plane and has an absolute value w=5|w|=5, write the complex number w in rectangular form.
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    Topic Notes
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    There are times when we are interested in obtaining a better understanding of the properties of a complex number, such as its argument and modulus. In this section, we will learn how to calculate the argument, also known as the angle, and the modulus, also known as the magnitude or the absolute value, of a complex number.
    Notes:

    Magnitude = modulus = absolute value
    z=a2+b2 |z|= \sqrt{a^2+b^2}

    Argument = angle
    arg(z)=θ arg(z)=\theta