Expressing as complex numbers

So the answer is 0.In summary, when expressing the expression (sqrt(-4) - 1)(sqrt(-9)) in the form a+ib, the answer is 3i. There is a sign ambiguity for the sqrt(-n) for n>0, but it could be either i*sqrt(n) or -i*sqrt(n). The answer to the problem (3+i)^2 - (3+i)^2 is 0.
  • #1
Ry122
565
2
How do I express the following in the form a+ib?

[tex] (\sqrt{-4} - 1) (\sqrt{-9}) [/tex]

My attempt:
(2i - 1)(3i)
6i-3i = 3i
 
Last edited:
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  • #2
Close, but (2i)(3i)=6i2=-6, not 6i.
 
  • #3
Can you tell me why the answer -6-+3i has plus or minus 3i?

Also can you tell me the answer to (3+i)^2 - (3+i)^2
The answer I got was 0.
9+6i+i^2-9-6i-i^2=0
 
Last edited:
  • #4
You have to define what you mean by sqrt(-n) for n>0. You could choose it to be either i*sqrt(n) or -i*sqrt(n). That's your sign ambiguity.
 
  • #5
Ry122 said:
Can you tell me why the answer -6-+3i has plus or minus 3i?
What was that the answer to?? Surely not the (2i-1)(3i) problem you were just talking about!

Also can you tell me the answer to (3+i)^2 - (3+i)^2
The answer I got was 0.
9+6i+i^2-9-6i-i^2=0
The answer to a2- a2 is 0 no matter what a is!
 

1. What is the definition of a complex number?

A complex number is a number that contains both a real part and an imaginary part, and can be expressed in the form a + bi, where a is the real part and bi is the imaginary part, with i representing the square root of -1.

2. Why do we use complex numbers?

Complex numbers are used to represent quantities that involve both real and imaginary components, such as electrical currents or waves. They also have many applications in mathematics, physics, and engineering.

3. What is the difference between real and imaginary parts of a complex number?

The real part of a complex number represents the horizontal axis on the complex plane, while the imaginary part represents the vertical axis. The real part is a normal number, while the imaginary part is a multiple of the imaginary unit i.

4. How do you express a complex number in polar form?

A complex number can be expressed in polar form as r(cosθ + isinθ), where r is the modulus (or magnitude) of the complex number and θ is the angle between the positive real axis and the vector representing the complex number on the complex plane.

5. Can complex numbers be added, subtracted, multiplied, and divided?

Yes, complex numbers can be added, subtracted, multiplied, and divided using the same rules as real numbers, with the added step of combining like terms of i. For division, the complex conjugate of the denominator is multiplied to eliminate the imaginary part in the denominator.

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