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First, let's make sure we are not confusing imaginary numbers with complex numbers.
Imaginary (sometimes called "pure imaginary" for clarity) numbers are numbers of the form ai, where a is a real number and i is the principal square root of -1.
To multiply two imaginary numbers ai and bi, start by pretending that i is a variable (like x).
So ai x bi = abi2. But since i is the square root of -1, i2=-1. So abi2=-ab.
For example, 6i x 7i =-42.
5i x 2i =-10.
(-5i) x 2i =-(-10)= 10.
Complex numbers are numbers of the form a+bi, where a and b are real numbers. a is the real part, bi is the imaginary part.
To multiply two complex numbers, again, just treat i as if it were a variable and then in the final answer, substitute -1 wherever you see i2.
Hence (a+bi)(c+di) = ac + adi + bci + dbi2 which simplifies to ac-db + (ad+bc)i.
For example:
(2+3i)(4+5i) = 8 + 10i +12i + 15i2= 8 + 10i + 12i - 15 = -7 + 22i
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Imaginary numbers examples?
An imaginary number is a number that cannot exist. An example of an imaginary number would be: the square root of negative nine, or any negative number. When I try to think of any two of the same numbers that would multiply together to be negative nine, all I can think of is 3 or -3. when I square both of those numbers, I get the number 9, not -9. When I multiply two negatives together, I get a positive number, therefore there is no possible way to get the square root of -9, or any negative number.
What is complex math?
Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.
What is an imaginary number and how is it expressed?
An imaginary number is a number that cannot exist. An example of an imaginary number would be: the square root of negative nine, or any negative number. When I try to think of any two of the same numbers that would multiply together to be negative nine, all I can think of is 3 or -3. when I square both of those numbers, I get the number 9, not -9. When I multiply two negatives together, I get a positive number, therefore there is no possible way to get the square root of -9, or any negative number.
What numbers are not real numbers?
The square root of any negative number is not a real number. denoted as i for imaginary because it does not exist, in the normal concept of numbers.Complex numbers (which include real and imaginary numbers) are combinations of real & imaginary numbers.While these numbers do not exist in the everyday concept of numbers, they are important in concepts of electricity and waves.
Is Every complex number is a pure imaginary number?
No. All Complex Numbers are of the form a + bi where a and b are Real Numbers and i is the square root of -1. So only ones where a = 0 are pure Imaginary Numbers.
