this is a very good question. lets solve (2+3i)/(4-2i). we want to make 4-2i real by multiplying it by the conjugate, or 4+2i (4-2i)(4+2i)=16-8i+8i+4=20, now we have (2+3i)/20 0r 1/10 + 3i/20 notice that -2i times 2i = -4i^2 =-4 times -1 = 4
The four roots are:1 + 2i, 1 - 2i, 3i and -3i.
if you mean both dimensions are complex numbers, then you use foil. Example (1+i)(1+2i)= 1 + 3i - 2 (since i2 = -1) -1+3i that's a rectangle but you should understand if your in a class with complex #
To add complex numbers, the real parts and the imaginary parts are added separately. For example, to add (3 + 3i) + (5 - 2i), the result is (3+5) + (3-2)i = 8+i. Subtraction is quite similar - you subtract the real and the imaginary parts separately. For example, (3 + 3i) - (5 - 2i) = (3-5) + (3 - -2)i = -2+5i.
(1+i)3 = 1 + 3i - 3 - i = -2 + 2i This is a complex number, and therefore cannot be plotted on a Cartesian plane.
(-2 + 3i) + (-1 - 2i) = -2 + 3i - 1 - 2i = -2 - 1 + 3i - 2i = -3 + i
this is a very good question. lets solve (2+3i)/(4-2i). we want to make 4-2i real by multiplying it by the conjugate, or 4+2i (4-2i)(4+2i)=16-8i+8i+4=20, now we have (2+3i)/20 0r 1/10 + 3i/20 notice that -2i times 2i = -4i^2 =-4 times -1 = 4
To multiply complex numbers you can use the same FOIL rule that you use for multiplying binomials (First, Inside, Outside, Last).(4 - 3i)(5 + 2i) = (4)(5) +(4)(2i) - (3i)(5) - (3i)(2i) = 20 + 8i-15i - 6(i)^2= 20 -7i - 6(-1) = 20 + 6 -7i = 26 -7i.
The four roots are:1 + 2i, 1 - 2i, 3i and -3i.
3i+2j)*(2i-3j)=0 bcz dot product is zero.
2
Expressions cannot be solved. Only equations or inequalities may be solved. Also, there is no symbol between 3i and 5.
All of them. Real numbers are a subset of complex numbers.
When adding and subtracting complex numbers, you can treat the "i" as any variable. For example, 5i + 3i = 8i, 5i -3i = 2i, etc.; (2 + 5i) - (3 - 3i) = (2 - 3) + (5 + 3)i = -1 + 8i.
7
-4-3i
5 + 2 i 2 -3 i = 0(i + 1)(2i - 5) = 0(i + 1) = 0, so, i = -1and(2i - 5) = 0, so, i = 5/2i two values are: -1 and 5/2