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Can a complex number be imaginary?
Yes, imaginary numbers are a subset of complex numbers.
Is the product of two imaginary numbers always a pure imaginary number?
no
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.
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
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 the product of two pure imaginary numbers a real number?
Yes it is.
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.
What are the kinds of complex numbers?
Complex numbers include real numbers, pure imaginary numbers, and the combination of those two.
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 operations will always produce a negative number?
Multiplication or division of two numbers of opposite signs: negative*positive, positive*negative, negative/positive, and positive/negative. Addition of two negative numbers: -5 + -2 = -7 Multiplying pure imaginary numbers of the same 'sign' : 5i * 2i = -10. -3i * -4i = -12. Dividing pure imaginary numbers of different signs (this comes from the fact that 1/i = -i, and i/i = +1)
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.
