If z satisfies the equation -z-z-1-2 i- then z is equal to A- 3-2-2 iC- 2-3-2D- 2-3-2

The correct option is B Let z = x + iy ∴ |z| z=1+2i ⇒√(x^2+y^2) (x+iy)=1+2i ⇒ ( √(x^2+y^2) x )+i( y)=1+2i ⇒√(x^2+y^2) x=1 and y= 2 If y= 2,√(x^2+4) x=1 ⇒ x^ ...

110

You visited us 110 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard VI

Mathematics

Writing Words in Numbers

If z satisfie...

Question

If z satisfies the equation |z| -z=1+2i, then z is equal to

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B
Let z = x + iy
$∴ | z | - z = 1 + 2 i$
$\Rightarrow \sqrt{x^{2} + y^{2}} - (x + i y) = 1 + 2 i$
$\Rightarrow (\sqrt{x^{2} + y^{2}} - x) + i (- y) = 1 + 2 i$
$\Rightarrow \sqrt{x^{2} + y^{2}} - x = 1 a n d y = - 2$
$I f y = - 2, \sqrt{x^{2} + 4} - x = 1$
$\Rightarrow x^{2} + 4 = (1 + x)^{2}$
$\Rightarrow 2 x = 3; x = \frac{3}{2}$
$∴ z = x + i y = \frac{3}{2} - 2 i$

Suggest Corrections

Similar questions

Q. The complex number

z

satisfying the equation

| z | = z + 1 + 2 i

Q. The complex number(s)

z

satisfying

R e (z^{2}) = 0

and

| z | = \sqrt{3}

is (are)

Q. If complex number

z

satisfies

| z | + z = 2 + i

, then

z

Q. If the complex number

z

satisfies

z + \sqrt{2} | z + 1 | + i = 0

, then

z

is :

Q. Complex number

z

satisfying the equation

z^{2} \times (1 + i) = - 7 + 17 i,

is/are

Join BYJU'S Learning Program

If z satisfies the equation |z| -z=1+2i, then z is equal to

The correct option is B Let z = x + iy ∴|z|−z=1+2i ⇒√x2+y2−(x+iy)=1+2i ⇒(√x2+y2−x)+i(−y)=1+2i ⇒√x2+y2−x=1 and y=−2 Ify=−2,√x2+4−x=1 ⇒x2+4=(1+x)2 ⇒2x=3;x=32 ∴z=x+iy=32−2i