- #1
vorcil
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4z + z(bar) = 5 + 9i
then z = [solve for this]
I don't know how to re arrange this equation
(5+9i)/4 = z+z(bar)
then z = [solve for this]
I don't know how to re arrange this equation
(5+9i)/4 = z+z(bar)
lurflurf said:z+z(bar)=2Re(z)
but written
4z + z(bar) = 5 + 9i
is not the same as
(5+9i)/4 = z+z(bar)
but
4(z + z(bar) )= 5 + 9i
is
Mentallic said:lurflurf, I can't see where you are headed with your approach.
[tex]4(z+\bar{z})=4z+4\bar{z} \neq 4z+\bar{z}[/tex]
vorcil take Dick's approach. Just remember that [itex]\bar{z}[/itex] is the complex conjugate of z, thus if z=a+ib then [itex]\bar{z}[/itex]=a-ib
A complex number is a number that is composed of two parts: a real number and an imaginary number. It can be written in the form a + bi, where a is the real part and bi is the imaginary part, with i being the imaginary unit.
A real number is a number that can be written without an imaginary part, while an imaginary number is a number that is multiplied by the imaginary unit i. Real numbers are located on the horizontal axis of a complex number plane, while imaginary numbers are located on the vertical axis.
To add or subtract complex numbers, you simply combine the real parts and then combine the imaginary parts. For example, (3 + 2i) + (5 + 4i) = (3+5) + (2i+4i) = 8 + 6i. You can also use the commutative property to rearrange the order of the numbers.
To multiply complex numbers, you use the FOIL method, which stands for First, Outer, Inner, Last. This means you multiply the first terms, then the outer terms, then the inner terms, and finally the last terms. For example, (3 + 2i)(5 + 4i) = 15 + 12i + 10i + 8i^2 = 15 + 22i - 8 = 7 + 22i.
To divide complex numbers, you use the concept of complex conjugates. This means you multiply the numerator and denominator by the complex conjugate of the denominator. For example, (3 + 2i) / (5 + 4i) = (3 + 2i)(5 - 4i) / (5 + 4i)(5 - 4i) = (15 - 12i + 10i - 8i^2) / (25 - 20i + 20i - 16i^2) = (15 - 2) / (25 + 16) = 13 / 41.