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For some practice working with complex numbers: Calculate $$(3 - 2i) + (4 + 4i) = \square$$ $$(3 - 2i) - (4 + 4i) = \square$$ $$(3 - 2i)(4 + 4i) = \square$$ The complex conjugate of $$(1 + i)$$ is $$(1 - i)$$. In general to obtain the complex conjugate reverse the sign of the imaginary part. (Geometrically this corresponds to finding the "mirror image" point in the complex plane by reflecting through the $x$-axis. The complex conjugate of a complex number $z$ is written with a bar over it: $$\bar{z}$$ and read as "$z$ bar". Notice that if $$z = a + ib$$, then $$(z)(\bar{z}) = |z|^2 = a^2 + b^2$$ which is also the square of the distance of the point $z$ from the origin. (Plot $z$ as a point in the "complex" plane in order to see this.) If $$z = 3 - 2i$$ then $$\bar{z} = \square$$ and $$|z| = \square$$ You can use this to simplify complex fractions. Multiply the numerator and denominator by the complex conjugate of the denominator to make the denominator real. $$\frac{3 - 2i}{4 + 4i} = \square + \square i$$ Two convenient functions to know about pick out the real and imaginary parts of a complex number. $$Re(a + ib) = a$$ (the real part (coordinate) of the complex number), and $$Im(a + ib) = b$$ (the imaginary part (coordinate) of the complex number. $$Re$$ and $$Im$$ are linear functions - now that you know about linear behavior you may start noticing it often.

          For some practice working with complex numbers:
Calculate
$$(3 - 2i) + (4 + 4i) = \square$$
$$(3 - 2i) - (4 + 4i) = \square$$
$$(3 - 2i)(4 + 4i) = \square$$
The complex conjugate of $$(1 + i)$$ is $$(1 - i)$$. In general to obtain the complex conjugate reverse the sign of the imaginary part. (Geometrically this corresponds to finding the "mirror image" point in the complex plane by reflecting through the $x$-axis. The complex conjugate of a complex number $z$ is written with a bar over it: $$\bar{z}$$ and read as "$z$ bar".
Notice that if $$z = a + ib$$, then
$$(z)(\bar{z}) = |z|^2 = a^2 + b^2$$
which is also the square of the distance of the point $z$ from the origin. (Plot $z$ as a point in the "complex" plane in order to see this.)
If $$z = 3 - 2i$$ then $$\bar{z} = \square$$ and $$|z| = \square$$
You can use this to simplify complex fractions. Multiply the numerator and denominator by the complex conjugate of the denominator to make the denominator real.
$$\frac{3 - 2i}{4 + 4i} = \square + \square i$$
Two convenient functions to know about pick out the real and imaginary parts of a complex number.
$$Re(a + ib) = a$$ (the real part (coordinate) of the complex number), and
$$Im(a + ib) = b$$ (the imaginary part (coordinate) of the complex number. $$Re$$ and $$Im$$ are linear functions - now that you know about linear behavior you may start noticing it often.

for some practice working with complex numbers calculate 3 2i 4 4i square 3 2i 4 4i square 3 2i4 4i square the complex conjugate of 1 i is 1 i in general to obtain the complex conjugate reve 69357

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