Recent questions in Complex Numbers

+2 votes

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asked Nov 30, 2023 in Complex Numbers by tapiwanashe (200 points)

+2 votes

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asked Nov 30, 2023 in Complex Numbers by tapiwanashe (200 points)

0 votes

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8. Let \( z_{1} \) and \( z_{2} \) be distinct randomly choosen roots of the equation \( z^{100}=1 \). The probability that \( \left|z_{1}+z_{2}\right| \geq \sqrt{2+\sqrt{3}} \) is expressed as \( \frac{p}{q} \) (where \( p \) and \( q \) are in their lowest form). Find \( (p+q) \).

asked Oct 27, 2023 in Complex Numbers by shlok0914 (70 points)

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1 answer

(1+i)⁴ (1+1/i)⁴

asked Oct 25, 2023 in Complex Numbers by tanayarajpure6188 (15 points)

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1 answer

Express the following fraction in x+iy form.

asked Oct 25, 2023 in Complex Numbers by Nnjdjjdjjejd (15 points)

+1 vote

1 answer

if √ x-iy = a-ib, prove that √ x+iy = a+ib

asked Oct 17, 2023 in Complex Numbers by orez (20 points)

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1 answer

If z=i-1, then zbar =

asked Oct 13, 2023 in Complex Numbers by samar0914 (15 points)

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1 answer

\( 8^{*} \). If \( Z_{1}, Z_{2}, Z_{3} \in C \) such that \[ \left|Z_{1}\right|=\left|Z_{2}\right|=\left|Z_{3}\right|=1 \text { and } \] \[ \frac{z_{1}^{2}}{z_{2} z_{3}}+\frac{z_{2}^{2}}{z_{1} z_{3}}+\frac{z_{3}^{2}}{z_{1} z_{2}}+1=0 \] then the integral values that \( \left|Z_{1}+Z_{2}+Z_{3}\right| \) can attain, is (1) 1 (2) 2 (3) 3 (4) 4

asked Aug 29, 2023 in Complex Numbers by 2134242345eqr (65 points)

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1 answer

Find the value of \( u \) and \( y \) of: \[ (x+i y)(2-3 i)=4+i \]

asked Jun 3, 2023 in Complex Numbers by frajem6410 (30 points)

0 votes

1 answer

Complex Numbers

asked May 28, 2023 in Complex Numbers by Atharva759 (15 points)

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1 answer

If \( \alpha \) and \( \beta \) are the roots of the equation \( x^{2}-x+1=0 \), then \( \alpha^{2009}+\beta^{2009}= \)

asked Mar 8, 2023 in Complex Numbers by kuldeep5288 (49 points)

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1 answer

Find the maximum and minimum values of the function \[ f(x)=x^{3}-9 x^{2}+24 x \].

asked Jan 24, 2023 in Complex Numbers by ganesh7064 (15 points)

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1 answer

Find the locus of |z - 1| + |z + 1 | ≤ 4.

asked Jan 13, 2023 in Complex Numbers by Syed Ali Raza (15 points)

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1 answer

Inequalities of complex numbers

asked Dec 11, 2022 in Complex Numbers by Hamzat20 (30 points)

+1 vote

1 answer

If one of the vertices of the square circumscribing the circle |z –1| = √2 is 2 + i√3, then which of the following can be a vertex of it?

asked Dec 10, 2022 in Complex Numbers by LuciferKrish (51.1k points)

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1 answer

The locus of the centre of a circle which touches the circles |z – z1| = a and |z – z2| = b externally is

asked Dec 10, 2022 in Complex Numbers by LuciferKrish (51.1k points)

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1 answer

If a, b, c and u, v, w are complex numbers representing the vertices of two triangles such that c = (1 – r)a + rb, w = (1 – r)u + rv,

asked Dec 10, 2022 in Complex Numbers by LuciferKrish (51.1k points)

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1 answer

A particle P starts from the point z0 = 1 + 2i. It moves first horizontally away from origin by 5 units and then vertically

asked Dec 10, 2022 in Complex Numbers by LuciferKrish (51.1k points)

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1 answer

A man walks a distance of 3 units from the origin towards the North-East (N45°E) direction. Form there, he walks a distance of 4 units

asked Dec 10, 2022 in Complex Numbers by LuciferKrish (51.1k points)

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1 answer

The shaded region where P = (–1, 0), Q = (–1 + √2, √2), R = (–1 + √2, –√2), S = (1, 0) is represented by

asked Dec 10, 2022 in Complex Numbers by LuciferKrish (51.1k points)

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