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Yes, the only argument would be the example, i + (-i) = 0. However, many people don't realize that 0 is both a purely real and pure imaginary number since it lies on both axes of the complex plane.

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โˆ™ 2010-11-21 10:03:35
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Q: Is the sum of two pure imaginary numbers always a pure imaginary number?
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Is the product of two imaginary numbers always a pure imaginary number?


Can a complex number be imaginary?

Yes, imaginary numbers are a subset of complex numbers.

A complex number might not be a pure imaginary number?

True. Complex numbers have a real part and an imaginary part. If either one of these is zero, the complex number will be a pure real or a pure imaginary.

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.

Is an imaginary number always sometimes or never a complex number?

Always. The set of imaginary numbers is a subset of complex numbers. Think of complex numbers as a plane (2 dimensional). The real numbers exist on the horizontal axis. The pure imaginary are the vertical axis. All other points on the plane are combinations of real and imaginary. All points on the plane (including imaginary axis and real axis) are complex numbers.

Can a number be imaginary but not pure imaginary?

Yes. The number 1 + i is imaginary but not pure imaginary, while 5i is pure imaginary.

Is every complex number a pure imaginary number?

No. For example the number 1+i. Pure imaginary complex numbers are of the form 0 + a*i, where a is a non-zero real number.

Can a complex number can't be a pure imaginary number?

A complex number can be a pure imaginary, or a pure real number, or a combination of the two. The form for a complex number is a + bi, where a & b can be any real numbers (so if a = 0, then the number is pure imaginary; and if b=0, then it is a real number).

What are pure imaginary numbers?

complex numbers with no real partif any complex number z can be written a + i bthen pure imaginary numbers have a=0 and b not equal to 0

Is the product of two pure imaginary numbers a real number?

Yes it is.

Are imaginary and complex numbers the same?

No. A complex number is a number that has both a real part and an imaginary part. Technically, a pure imaginary number ... which has no real part ... is not a complex number.

Is the difference of a complex number and its conjugate a real imaginary or pure imaginary number?

It is a pure imaginary number.Since (a+bi)-(a-bi) = 2bi, it is a pure imaginary number (it has no real component).

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