Answer:
![\boxed{7-26i}](https://tex.z-dn.net/?f=%5Cboxed%7B7-26i%7D)
Step-by-step explanation:
The binomials are multiplied in the usual way, using FOIL or the distributive property:
(5 -2i)(3 -4i) = 15 -20i -6i +8i²
Since i² = -1, this becomes ...
= 15 -20i -6i -8 = 7 -26i
The answer is: (z - 6)(z + 15)
z² + 9z - 90 = z*z + 15z - 6z - 6*15 =
= (z*z + 15z) - (6z + 6*15) =
= z(z + 15) - 6(z + 15) =
= (z - 6)(z + 15)
Correct answer is: distance from D to AB is 6cm
Solution:-
Let us assume E is the altitude drawn from D to AB.
Given that m∠ACB=120° and ABC is isosceles which means
m∠ABC=m∠BAC = ![\frac{180-120}{2}=30](https://tex.z-dn.net/?f=%5Cfrac%7B180-120%7D%7B2%7D%3D30)
And AC= BC
Let AC=BC=x
Then from ΔACD , cos(∠ACD) = ![\frac{DC}{AC} =\frac{4}{x}](https://tex.z-dn.net/?f=%5Cfrac%7BDC%7D%7BAC%7D%20%3D%5Cfrac%7B4%7D%7Bx%7D)
Since DCB is a straight line m∠ACD+m∠ACB =180
m∠ACD = 180-m∠ACB = 60
Hence ![cos(60)=\frac{4}{x}](https://tex.z-dn.net/?f=cos%2860%29%3D%5Cfrac%7B4%7D%7Bx%7D)
![x=\frac{4}{cos60}= 8](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B4%7D%7Bcos60%7D%3D%208)
Now let us consider ΔBDE, sin(∠DBE) = ![\frac{DE}{DB} =\frac{DE}{DA+AB} = \frac{DE}{4+8}](https://tex.z-dn.net/?f=%5Cfrac%7BDE%7D%7BDB%7D%20%3D%5Cfrac%7BDE%7D%7BDA%2BAB%7D%20%3D%20%5Cfrac%7BDE%7D%7B4%2B8%7D)
![DE = 12sin(30) = 6cm](https://tex.z-dn.net/?f=DE%20%3D%2012sin%2830%29%20%3D%206cm)