If the axes are shifted to the point (1, - 2) without solution, then the equation 2x² + y² - 4x + 4y = 0 becomes

• 2X² + 3Y² = 6

• 2X² + Y²

• X² + 2Y²

• None of the above

In a group ( G, *), then equation x * a = b has a

• unique solution b * a^-1

• unique solution a^-1 * b

• unique solution a^-1 * b^-1

• many solutions

223.

The number of solutions of the equation sin(e^x) = 5^x + 5^-x,  is

• 0

• 1

• 2

• infinitely many

If z satisfies the equation $\left|\mathrm{z}\right|$ - z = 1 + 2i, then z is equal to

• $\frac{3}{2} + 2\mathrm{i}$

• $\frac{3}{2} - 2\mathrm{i}$

• $2 - \frac{3}{2}\mathrm{i}$

• $2 + \frac{3}{2}\mathrm{i}$

If $\mathrm{z} = \frac{1 - \mathrm{i}\sqrt{3}}{1 + \mathrm{i}\sqrt{3}}$, then arg (z) is

• 60°

• 120°

• 240°

• 300°

For what values of m can the expression 2x² + mxy + 3y² - 5y - 2 be expressed as the product of two linear factors?

• 0

• $\pm 1$

• $\pm 7$

• 49

If n is an integer which leaves remainder one when divided by three, then ${\left(1 + \sqrt{3}\mathrm{i}\right)}^{\mathrm{n}} + {\left(1 - \sqrt{3}\mathrm{i}\right)}^{\mathrm{n}}$ equals

• - 2^{n + 1}

• 2^{n + 1}

• - (- 2)ⁿ

• - 2ⁿ

If $\left|\frac{\mathrm{z} - 25}{\mathrm{z} - 1}\right| = 5$,  find the value of $\left|\mathrm{z}\right|$

• 3

• 4

• 5

• 6

Argument of the complex number $\left(\frac{- 1 - 3\mathrm{i}}{2 +\hspace{0.17em}\mathrm{i}}\right)$ is

• 45°

• 135°

• 225°

• 240°

The number of real roots of the equation ${\mathrm{x}}^4 + \sqrt{{\mathrm{x}}^4 + 20} = 22$ is

• 4

• 2

• 0

• 1