Complex Numbers
Complex Numbers
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The square root of −1 is represented by the symbol i. It is read as iota.
i = or i2 = −1 -
Any number of the form a + ib, where a and b are real numbers, is known as a complex number. A complex number is denoted by z.
z = a + ib -
For the complex number z = a + ib, a is the real part and b is the imaginary part. The real and imaginary parts of a complex number are denoted by Re z and Im z respectively.
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For complex number z = a + ib, Re z = a and Im z = b
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A complex number is said to be purely real if its imaginary part is equal to zero, while a complex number is said to be purely imaginary if its real part is equal to zero.
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For e.g., 2 is a purely real number and 3i is a purely imaginary number.
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Two complex numbers are equal if their corresponding real and imaginary parts are equal.
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Complex numbers z1 = a + ib and z2 = c + id are equal if a = c and b = d.
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- Let's now try and solve the following puzzle to check whether we have understood this concept.
Solved Exampl…
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