Trying to find the right answer to this..

1 + i 2 + i 4 + i 6 + .....+ i 20 = (1 + i 2 ) + (1 +i 4 ) + (1 + i 6 ) + (1 + i 8 ) + (1 +i 10 ) + (1 +i 12 ) + (1 +i 14 ) + ( 1 +i 16 ) + (1 + i 18 ) + i 20 = (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + 1. = 1 ( ∴ i 4 = i 8 = i 12 = i 16 = i 20 = 1, i 2 = -1)

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Complex Numbers and Quadratic Equations

Short Answer Type

21.

solve each of the following equations:

x²+ 3 = 0

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22.

solve each of the following equations:

2x²+ x + 1 = 0

120 Views

23.

solve each of the following equations:

$space space space space space space square root of 2 space straight x squared space plus space straight x space plus space square root of 2 space equals space 0$

115 Views

24.

Solve each of the following equations:

$space space space space space space space space space space straight x squared space plus space straight x space plus space fraction numerator 1 over denominator square root of 2 end fraction equals space 0$

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25.

Write the following complex numbers in polar form and hence, find their modulus and argument.

$space space space space space space space space space space space space space 1 half minus fraction numerator square root of 3 over denominator 2 end fraction straight i$

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26.

If z₁- -3x + 2iy and z₂ = 6 -5i are equal, find value of x and y.

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27.

If Z₁= (x - 3y) - i (2x + y), and Z₂= -1 - 5i are equal, find values of x a nd y.

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28.
Evaluate :

1 + i² + i⁴ + i⁶+ .....+ i²⁰

1 + i² + i⁴ + i⁶+ .....+ i²⁰ = (1 + i²) + (1 +i⁴) + (1 + i⁶ ) + (1 + i⁸ ) + (1 +i¹⁰ ) + (1 +i¹² ) + (1 +i¹⁴ ) + ( 1 +i¹⁶) + (1 + i¹⁸ ) + i²⁰

= (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + (1 - 1) + 1.

= 1 (∴ i⁴ = i⁸= i¹²= i¹⁶= i²⁰= 1, i²= -1)