If a complex number has arg(z) = and the product of real and imaginary part is 3√3, find the conjugate of the complex number z.

Question

Question

Answer 1

Concept:

Let z = x + iy be a complex number.

Calculation:

Let z = x + iy

According to the question

arg(z) =

⇒

⇒ y = x

Also given xy = 3

⇒ y =

Comparing the values of y, we get

⇒

⇒ x² = 3

⇒ x = ±

∴ x = {∵ arg(z) lies in first quadrant so -ve value is neglected}

Also y = x = 3

Complex number z = x + iy = + 3i

Conjugate of z = (z̅) = - 3i

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