Complex Numbers: Level 3 Challenges Practice Problems Online

If the square of $x$ and the square root of $x$ are equal to each other, but not equal to $x$ , then what is the value of $x^2+x$ ?

Let $z=x+iy$ be a complex number where $x$ and $y$ are integers. Find the area of the rectangle whose vertices are the roots of the equation $\large z \bar{z}^3+\bar{z}z^3=350.$

Details: $\bar{z}=x-iy$ and $i=\sqrt{-1}$ .

How many complex numbers are the conjugate of their own cube?

The complex numbers $p$ and $q$ satisfy $p^3=5+i\sqrt{2}$ and $q^3=5-i\sqrt{2}$ .

Find the only possible integer value of $p+q$ .

$\large e ^{ i\theta }e^{ 2i\theta} e^{ 3i\theta }...\large e^{ ni\theta } = 1$

Find the value of $\theta$ satisfying the above equation for $m\in\mathbb{N}$ .

\frac { 2m\pi }{ { n }^{ 2 } }

\frac { 2n\pi }{ m(m+1) }

\frac { m\pi }{ { n }^{ 2 } }

\frac { m\pi }{ n(n+1) }

\frac { 2m\pi }{ n(n+1) }

\frac { 4m\pi }{ n(n+1) }

\frac { n\pi }{ { m }^{ 2 } }

\frac { 4m\pi }{ { n }^{ 2 } }

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Complex Numbers: Level 3 Challenges