Quiz complex numbers

  • How do you identify complex numbers?

    A complex number is expressed in standard form when written a+bi where a is the real part and bi is the imaginary part.
    For example, 5+2i is a complex number.
    So, too, is 3+4√3i.
    Imaginary numbers are distinguished from real numbers because a squared imaginary number produces a negative real number..

  • What is the use of complex numbers in real life?

    Complex numbers (the sum of real and imaginary numbers) occur quite naturally in the study of quantum physics.
    They're useful for modelling periodic motions (such as water or light waves) as well as alternating currents..

  • Complex conjugates give us another way to interpret reciprocals.
    You can easily check that a complex number z = x + yi times its conjugate x – yi is the square of its absolute value z2.
    Therefore, 1/z is the conjugate of z divided by the square of its absolute value z2.
  • In fact, one of the most helpful aspects of the complex conjugate is to test if a complex number z = a + bi is real.
    A complex number is real if and only if z = a +0i; in other words, a complex number is real if it has an imaginary part of 0.
  • The absolute value of the complex number, 2i, is 2.
    We can put the complex number, 2i, in the form a + bi by letting a = 0.
    That is, 2i = 0 + 2i.
    Therefore, a = 0 and b = 2.
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