Question

ᴩʟᴇᴀꜱᴇ ꜱᴏʟᴠᴇ ᴛʜᴇꜱᴇ qᴜᴇꜱᴛɪᴏɴꜱ ꜰᴏʀ ᴍᴇ ɢᴜyꜱ : ( ᴡɪᴛʜ ꜱᴛᴇᴩꜱ)
(i) 15 ( x - y ) - 20 ( y - x)²
(ii) z ( z + 5 ) + 7 ( z + 5 )
ᴄʟᴀꜱꜱ 8 : ꜰᴀᴄᴛᴏʀɪᴢᴀᴛɪᴏɴ ᴏꜰ ᴀʟɢᴇʙʀᴀɪᴄ ᴇxᴩʀᴇꜱꜱɪᴏɴꜱ
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Answer 1

Answer:

1st = Equation at the end of step 1

(15 • (x - y)) - 20 • (y - x)2

STEP2:Equation at the end of step 2

15 • (x - y) - 20 • (y - x)2

STEP3:Pulling out like terms

 3.1      Pull out     x-y 

Note that  y-x =(-1)• x-y 

After pulling out, we are left with :

      (x-y) • ( 15  *  (-1) +( 20  *  (y-x) ))

STEP4:Pulling out like terms

 4.1     Pull out like factors :

   -20x + 20y - 15  =   -5 • (4x - 4y + 3) 

Final result :

-5 • (x - y) • (4x - 4y + 3)

2nd=

11th

Maths

Complex Numbers and Quadratic Equations

Algebra of Complex Numbers

If z is a non - real comple...

MATHS

If z is a non-real complex number, then the minimum value of (Imz)5Imz5 is

A

-2

B

-4

C

-5

D

-1

HARD

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VIDEO EXPLANATION



ANSWER

z is a non-real complex number.

let z=reiθ

(Imz)5Imz5=r5sin5θr5sin5θ

say, f(θ)=sin5θsin5θ

equating first derivative to 0

f′(θ)=0

⇒sin5θ⋅5cos5θ−sin5θ⋅5sin4θ⋅cosθ

⇒sinθ⋅cos5θ=cosθ⋅sin5θ

⇒tanθ=tan5θ

⇒θ=0,π/4...

but f(0) is indeterminate

f(π/4)=−4

∴ Minimum value of 

Step-by-step explanation:

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