# Solve the system of equations Re(z2) = 0, z = 2. - Mathematics

Sum

Solve the system of equations Re(z2) = 0, z = 2.

#### Solution

Given that: Re(z2) = 0, z = 2

Let z = x + yi

∴ |z| = sqrt(x^2 + y^2)

⇒ sqrt(x^2 + y^2) = 2

⇒ x2 + y2 = 4  .....(i)

Since, z = x + yi

z2 = x2 + y2 i2 + 2xyi

⇒ z2 = x2 – y2 + 2xyi

∴ Re(z2) = x2 – y2

⇒ x2 – y2 = 0  ....(ii)

From equation (i) and (ii), we get

x2 + y2 + x2 − y2 = 4 + 0

⇒ 2x2 = 4

⇒ x2 = 2

⇒ x = +-  sqrt(2) and y = +-  sqrt(2)

Hence, z = sqrt(2) +- isqrt(2), -sqrt(2) +- isqrt(2).

Concept: The Modulus and the Conjugate of a Complex Number
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#### APPEARS IN

NCERT Mathematics Exemplar Class 11
Chapter 5 Complex Numbers and Quadratic Equations
Exercise | Q 21 | Page 92

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