Question

Which of the following statements is not true?
A. Every real number is also a complex number
B. In order for a+bi to be a complex number, b must be nonzero
C. The variable z is often used to denote a complex number
D. A complex number is a number that can be written in the form a+bi where a and b are real numbers

Answer 1

option D

Answer 2

@dan815

Answer 3

Wrong, it's option c

Answer 4

No, c is correct. You often see z = x+iy.

Answer 5

No, you use i to denote a complex number.

Answer 6

A, B, and D are correct, so what choices do we have left?

Answer 7

The reals are a subset of the complex numbers, so every real number is also a complex number. I don't need i in order to have a complex number.

Answer 8

@steve816 That's not right. "Denote" in this context means symbolize. 'i' doesn't denote a complex number, it *is* one.

Answer 9

its optionD

Answer 10

Because the real numbers are a subset of the complex numbers, A is true. Even the number 3 can be considered a complex number. 3, for example, is simply a + bi where a = 3 and b = 0.

Based on the argument above, if the real numbers are a subset of the complex numbers (as in every real number is also a complex number), then why would b need to be nonzero? I just gave an example where b = 0.

z is most definitely used to represent a complex number. You will very often see f(z) = x + iy. Or a complex number \(z_{o} = x_{0} + iy_{0}\). This is common notation.

D is correct as well. a +bi is the general form of a complex number. a and b are real numbers where a is the "real" part and b is the "imaginary" part. Theyre still real numbers in and of themselves, though.

Answer 11

Well, a more general form of a complex function would actually be something like :
\(f(z) = u(x,y) + iv(x,y)\)
Either way, z is definitely used, so C is fine.

Answer 12

\(B\) is the answer. All real numbers are complex, so that \(a+bi\) need not have \(b\ne 0\).

Answer 13

A is true so B must be untrue