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

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no

Yes, imaginary numbers are a subset of complex numbers.

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.

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).

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

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no

Yes, imaginary numbers are a subset of complex numbers.

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.

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.

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.

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).

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

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

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.

A complex number is a number of the form a + bi, where a and b are real numbers and i is the principal square root of -1. In the special case where b=0, a+0i=a. Hence every real number is also a complex number. And in the special case where a=0, we call those numbers pure imaginary numbers. Note that 0=0+0i, therefore 0 is both a real number and a pure imaginary number. Do not confuse the complex numbers with the pure imaginary numbers. Every real number is a complex number and every pure imaginary number is a complex number also.

If you are talking about pure imaginary numbers (a complex number with no real part) then no. Example: bi times ci where b and c are real numbers equals b*c*iÂ² = b*c*(-1) = -b*c, which is a real number, because b & c & -1 are all real numbers. If you're talking about multiplying two complex numbers (a + bi)*(c + di), then the product will be complex, but it could be real or imaginary, depending on the values of a, b, c, & d.

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