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Represent the complex numbers 2-2i...

Represent the complex numbers
`2-2i`

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To represent the complex number \( 2 - 2i \) on the complex plane, we follow these steps: ### Step 1: Identify the real and imaginary parts The complex number is given as \( 2 - 2i \). Here, the real part \( a \) is \( 2 \) and the imaginary part \( b \) is \( -2 \). ### Step 2: Draw the complex plane Draw a two-dimensional Cartesian coordinate system. The horizontal axis represents the real part, and the vertical axis represents the imaginary part. ### Step 3: Mark the real part on the real axis Locate the point \( 2 \) on the horizontal (real) axis. This is where the real part of the complex number is represented. ### Step 4: Mark the imaginary part on the imaginary axis Locate the point \( -2 \) on the vertical (imaginary) axis. This represents the imaginary part of the complex number. ### Step 5: Plot the point From the point \( 2 \) on the real axis, move vertically down to \( -2 \) on the imaginary axis. Mark this point. The coordinates of this point are \( (2, -2) \). ### Step 6: Label the point Label the point as \( 2 - 2i \) to indicate that it represents the complex number. ### Final Representation The complex number \( 2 - 2i \) is represented by the point \( (2, -2) \) on the complex plane. ---
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ICSE-COMPLEX NUMBERS-Chapter Test
  1. Represent the complex numbers 2-2i

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  2. Find the square root of 5-12i

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  3. Find the locus of a complex number z=x +yi, satisfying the relation |z...

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  4. Express (13i)/(2-3i) in the form A + Bi

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  5. If z= x +yi and (|z-1-i|+4)/(3|z-1-i|-2)=1, show that x^(2) + y^(2) -2...

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  6. If omega and omega^(2) are cube roots of unity, prove that (2- omega +...

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  7. If z(1), z(2) in C (set of complex numbers), prove that |z(1) + z(2)| ...

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  8. If z = x + yi, omega = (2-iz)/(2z-i) and |omega|=1, find the locus of ...

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  9. Simplify: (1- 3omega + omega^(2)) (1 + omega- 3omega^(2))

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  10. Find the locus of z satisfying |(z-3)/(z+1)|=3 in the complex plane.

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  11. Given that (2 sqrt3 cos 30^(@) - 2i sin 30^(@))/(sqrt2 (cos 45^(@) + i...

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  12. Simplify : (1- omega) (1- omega^(2)) (1- omega^(4)) (1- omega^(8))

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  13. Find the locus of a complex number z= x + yi, satisfying the relation ...

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  14. Find the real values of x and y satisfying the equality (x-2 + (y-3)i)...

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  15. If i= (sqrt-1), prove that following (x+1+i) (x+ 1-i) (x-1-i) (x-1+ i)...

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  16. If z= x + yi and |2z + 1| = |z- 2i|, show that 3(x^(2) + y^(2)) + 4(x-...

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  17. Find the amplitude of the complex number "sin" (6pi)/(5) + i (1- "cos"...

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  18. Express (1- 2i)/(2+i) + (3+i)/(2-i) in the form a + bi

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  19. Find the value of x and y given that (x + yi) (2-3i)=4+i

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  20. If the ratio (z-i)/(z-1) is purely imaginary, prove that the point z l...

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  21. If (-2 + sqrt-3) (-3 + 2 sqrt-3) = a + bi, find the real numbers a and...

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