Question

10. If 5(2-3) -4(2-2) = 0, then the value of z is:​

Answer 1

Answer:

z is the real number

Step-by-step explanation:

z−5i

=1

⇒

x+iy+5i

x+iy−5i

=1

⇒

x+i(y+5)

x+i(y−5)

=1

⇒

∣

∣

∣

∣

∣

x+i(y+5)

x+i(y−5)

×

x−i(y+5)

x−i(y+5)

∣

∣

∣

∣

∣

=1

⇒

x

2

+(y+5)

2

x

2

+i(y−5)x−ix(y+5)+y

2

−25

=1

⇒x

2

+i(yx−5x−xy−5x)+y

2

−25=x

2

+y

2

+10y+25

⇒+i(−5x−5x)−25=10y+25

⇒−10ix−10y=50

⇒−i(x+iy)=5

⇒x+iy=

−i

5

×

i

i

=5i

Comparing the real and imaginary parts we get

∴x=0,y=5

∴z=0+5i=5i