$\frac{\sqrt{5+12i}+\sqrt{5-12i}}{\sqrt{5+12i}-\sqrt{5-12i}}=$

Important Questions on Complex Numbers

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>EXERCISE>Q 2

The roots of the equation ${\left(x-1\right)}^3+8=0$ are

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>EXERCISE>Q 3

If ${\left(-7-24i\right)}^{\frac{1}{2}}=x-iy$ then $x^2+y^2=$

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>EXERCISE>Q 4

If ${\left(\frac{1+i\sqrt{3}}{1-i\sqrt{3}}\right)}^n$ is an integer, then $n$ is

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>EXERCISE>Q 5

${\left(1+2\omega +{\omega }^2\right)}^{3n}-{\left(1+\omega +2{\omega }^2\right)}^{3n}=$

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>EXERCISE>Q 6

If $\omega$ is a complex cube root of unity, then $225+{\left(3\omega +8{\omega }^2\right)}^2+{\left(3{\omega }^2+8\omega \right)}^2$ is equal to

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>EXERCISE>Q 7

If $\omega$ is an imaginary cube root of unity, then find the value of $\left(1+\omega \right)\left(1+{\omega }^2\right)\left(1+{\omega }^3\right)\left(1+{\omega }^4\right)\left(1+{\omega }^5\right).......\left(1+{\omega }^{3n}\right)$.

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Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>EXERCISE>Q 8

If $x^2+x+1=0$, then find the value of $\sum _{r=1}^{27}{\left(x^r+\frac{1}{x^r}\right)}^2$.

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IMPORTANT

Gamma Question Bank for Engineering Mathematics>Chapter 5 - Complex Numbers>EXERCISE>Q 9

Find the value of $4+5{\left(-\frac{1}{2}+\frac{i\sqrt{3}}{2}\right)}^{334}+3{\left(-\frac{1}{2}+\frac{i\sqrt{3}}{2}\right)}^{365}$.