This is a free lesson from our course in Algebra II
In this lesson you'll be introduced to basics of complex numbers and concept of an imaginary unit. Further it explains how to find the
value of any expression of an imaginary unit.
A complex number is made up of both real and imaginary components. It can be represented
by an expression of the form (a + bi), where a
and b are real numbers and i is imaginary. The number i is
defined as the square root of -1, denoted as -1.
It is an imaginary number, since the
square root of any negative number is not a real number.Then we can think of i2 as -1. Remember complex numbers are not algebraic expressions. They are numbers, containing a real part (a) and an imaginary part (bi).
(More text below video...)
(Continued from above)
E.g. complex number C
= 5 + 2i has real part of 5 and the imaginary part would be 2i.
To find the value of i raised to the powers, it has a repeating pattern.
When i is raised to any whole number power, the result is always 1, i,
-1 or -i.
If the exponent on i is divided by 4, the remainder will
indicate which of the four values the result is 1, i, -1 or -i.
To simplify an expression having i raised to power n (n
> 4), remember to divide n by 4 and raise i to the remainder
of division, which yields value of i.
For example, find the value of i370. First divide 370 by 2, which gives remainder as 2. Now raise i to 2 i.e. i2, which gives -1. So value of i370=
-1.
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-1.
It is an imaginary number, since the
square root of any negative number is not a real number.Then we can think of i2 as -1. Remember complex numbers are not algebraic expressions. They are numbers, containing a real part (a) and an imaginary part (bi).