Find the product z1z2 in standard form. (Simplify your answer completely.) z1 = 9 + 3i, z2 = −9 + 3i

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Step-by-step explanation:

These are "complex numbers" because they have the imaginary number, i, in the expression.

The 9 (and the -9) is the real part and the 3i is the imaginary part. But when you add or subtract, multiply or divide them you can manipulate them just as if the i was a variable (like x or n or y) If you learned to multiply

(x+2)(x+5)

= x^2 + 7x + 10

This problem will work the same way. You may have learned "FOIL" or using a box to multiply two binomials (two-piece things like x+2)

**SUPER IMPORTANT NOTE: i^2 is equal to -1

These particular complex numbers are called conjugates which means they have the same 'pieces' the 9 and the 3i, with only one sign different. So there is a short cut for this problem and the imaginary number falls out and we get a real number answer. This doesn't happen for every question, only when you multiply conjugates, but the method shown here works for multiplying complex numbers all the time.

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

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step-by-step explanation:

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