1) write the sum or difference in the standard form a + bi. (2 points) ( 7 + 5i) - ( -9 + i) a) 16+4i b) -16-4i c) 16-4i d) -2+6i 2) write the product in standard form. (2 points) ( 7 + 7i)( 6 + 7i) a) -7 + 91i b) 49i2 + 91i + 42 c) 91 - 7i d) -7 - 91i 3) find the product of the complex number and its conjugate. (2 points) 1 + 3i a) 1 + 9i b) 10 c) -8 d) 1-9i 4) write the expression in standard form. (2 points) three divided by quantity three minus twelve i. a) - one divided by seventeen. + four divided by seventeen. i b) one divided by seventeen. - four divided by seventeen. i c) - one divided by seventeen. - four divided by seventeen. i d) one divided by seventeen. + four divided by seventeen. i 5) find the real numbers x and y that make the equation true. (2 points) 5 + yi = x + 3i

When performing addition and multiplication with constant numbers, we treat i as we would treat any variable x in an expression, with the same rules and properties of addition and multiplication.

1)



2)
Distribute 7+7i over 6 and 7i:



collecting similar terms, and substituting  with -1 we have:

42+91i-49=-7+91 i

3)

The conjugate of a complex number a+bi is a-bi;
the conjugate of 1+3i is 1-3i.

Thus, using the difference of squares formula we have



4)

To write a rational expression ( with a complex number in the denominator) in the standard form, we multiply by the conjugate of the denominator both the numerator and the denominator:





simplifying by 9, the complex number is finally written as 



5)

2 complex numbers a+bi, and c+di are equal only if a=c, and b=d. (Where a, b, c, d are real numbers.)

Thus, x=5, and y=3 is the solution to the equation.

Answers:

1) A
2) A
3) B
4) D
5) (x, y) =( 5, 3)