Concepts of Complex Numbers
Complex Numbers and Quadratic Equation

117501 Value of \(\frac{(\cos \theta+i \sin \theta)^4}{(\cos \theta-i \sin \theta)^3}\) is

1 \(\cos 5 \theta+\mathrm{i} \sin 5 \theta\)
2 \(\cos 7 \theta+i \sin 7 \theta\)
3 \(\cos 4 \theta+\mathrm{i} \sin 4 \theta\)
4 \(\cos \theta+\mathrm{i} \sin \theta\)
Complex Numbers and Quadratic Equation

117502 If \(z=x+i y, z^{1 / 3}=\mathbf{a}-\mathbf{i b}\),
then \(\frac{x}{a}-\frac{y}{b}=k\left(a^2-b^2\right)\) where \(k\) is equal to

1 1
2 2
3 3
4 4
Complex Numbers and Quadratic Equation

117506 If the complex numbers \(z_1, z_2\) and \(z_3\) are in \(A P\), then they lie on a

1 a circle
2 a parabola
3 line
4 ellipse
Complex Numbers and Quadratic Equation

117507 Amplitude of \(\frac{1+\sqrt{3} i}{\sqrt{3}+1}\) is:

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
Complex Numbers and Quadratic Equation

117501 Value of \(\frac{(\cos \theta+i \sin \theta)^4}{(\cos \theta-i \sin \theta)^3}\) is

1 \(\cos 5 \theta+\mathrm{i} \sin 5 \theta\)
2 \(\cos 7 \theta+i \sin 7 \theta\)
3 \(\cos 4 \theta+\mathrm{i} \sin 4 \theta\)
4 \(\cos \theta+\mathrm{i} \sin \theta\)
Complex Numbers and Quadratic Equation

117502 If \(z=x+i y, z^{1 / 3}=\mathbf{a}-\mathbf{i b}\),
then \(\frac{x}{a}-\frac{y}{b}=k\left(a^2-b^2\right)\) where \(k\) is equal to

1 1
2 2
3 3
4 4
Complex Numbers and Quadratic Equation

117506 If the complex numbers \(z_1, z_2\) and \(z_3\) are in \(A P\), then they lie on a

1 a circle
2 a parabola
3 line
4 ellipse
Complex Numbers and Quadratic Equation

117507 Amplitude of \(\frac{1+\sqrt{3} i}{\sqrt{3}+1}\) is:

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
Complex Numbers and Quadratic Equation

117501 Value of \(\frac{(\cos \theta+i \sin \theta)^4}{(\cos \theta-i \sin \theta)^3}\) is

1 \(\cos 5 \theta+\mathrm{i} \sin 5 \theta\)
2 \(\cos 7 \theta+i \sin 7 \theta\)
3 \(\cos 4 \theta+\mathrm{i} \sin 4 \theta\)
4 \(\cos \theta+\mathrm{i} \sin \theta\)
Complex Numbers and Quadratic Equation

117502 If \(z=x+i y, z^{1 / 3}=\mathbf{a}-\mathbf{i b}\),
then \(\frac{x}{a}-\frac{y}{b}=k\left(a^2-b^2\right)\) where \(k\) is equal to

1 1
2 2
3 3
4 4
Complex Numbers and Quadratic Equation

117506 If the complex numbers \(z_1, z_2\) and \(z_3\) are in \(A P\), then they lie on a

1 a circle
2 a parabola
3 line
4 ellipse
Complex Numbers and Quadratic Equation

117507 Amplitude of \(\frac{1+\sqrt{3} i}{\sqrt{3}+1}\) is:

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
Complex Numbers and Quadratic Equation

117501 Value of \(\frac{(\cos \theta+i \sin \theta)^4}{(\cos \theta-i \sin \theta)^3}\) is

1 \(\cos 5 \theta+\mathrm{i} \sin 5 \theta\)
2 \(\cos 7 \theta+i \sin 7 \theta\)
3 \(\cos 4 \theta+\mathrm{i} \sin 4 \theta\)
4 \(\cos \theta+\mathrm{i} \sin \theta\)
Complex Numbers and Quadratic Equation

117502 If \(z=x+i y, z^{1 / 3}=\mathbf{a}-\mathbf{i b}\),
then \(\frac{x}{a}-\frac{y}{b}=k\left(a^2-b^2\right)\) where \(k\) is equal to

1 1
2 2
3 3
4 4
Complex Numbers and Quadratic Equation

117506 If the complex numbers \(z_1, z_2\) and \(z_3\) are in \(A P\), then they lie on a

1 a circle
2 a parabola
3 line
4 ellipse
Complex Numbers and Quadratic Equation

117507 Amplitude of \(\frac{1+\sqrt{3} i}{\sqrt{3}+1}\) is:

1 \(\frac{\pi}{6}\)
2 \(\frac{\pi}{4}\)
3 \(\frac{\pi}{3}\)
4 \(\frac{\pi}{2}\)
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