Question

More help with math question answer all 5 correctly please!!

Answer 1

See below for answers and explanation

Explanation:

Problem 1

`z_1z_2=(3+3i)(-4+0i)=(3)(-4)+(3)(0i)+(3i)(-4)+(3i)(0i)=-12-12i`

So, your best answer is Q

Problem 2

A complex number,
`z=a+bi`, has a conjugate of
`z=a-bi` and vice versa. Thus, your best answer is P

Problem 3

`z_1-z_2=(-5+1i)-(3+5i)=-5+i-3-5i=-8-4i`

So, your best answer is R

Problem 4

To divide two complex numbers, multiply the numerator and denominator by the denominator's conjugate and simplify:

`(4+7i)/(2-6i)\\\\(4+7i)/(2-6i)*(2+6i)/(2+6i)\\\\((4)(2)+(4)(6i)+(7i)(2)+(7i)(6i))/((2)(2)+(2)(6i)+(-6i)(2)+(-6i)(6i))\\\\(8+24i+14i+42i^2)/(4+12i-12i-36i^2)\\\\(8+38i+42(-1))/(4-36(-1))\\\\(8+38i-42)/(4+36)\\\\(-34+38i)/(40)\\\\-(34)/(40)+(38)/(40)i\\ \\-(17)/(20)+(19)/(20)i`

Thus, the correct answer is D

Problem 5

`z_T=(z_1z_2)/(z_1+z_2)\\ \\z_T=((70+40i)(50-35i))/((70+40i)+(50-35i))\\\\z_T=((70)(50)+(70)(-35i)+(40i)(50)+(40i)(-35i))/(70+40i+50-35i)\\\\z_T=(3500-2450i+2000i-1400i^2)/(120+5i)\\\\z_T=(3500-450i-1400(-1))/(120+5i)\\\\z_T=(3500-450i+1400)/(120+5i)\\\\z_T=(4900-450i)/(120+5i)`

`z_T=(4900-450i)/(120+5i)*(120-5i)/(120-5i)\\\\z_T=(585750-78500i)/(14425)\\\\z_T=(23430)/(577)-(3140i)/(577)\\\\z_T\approx40.607-5.442i`

Therefore, the correct answer is B