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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

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23.

solve each of the following equations:

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

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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.

Here, Z₁= -3x+ 2iy and Z₁= 6 - 5i

Now,    Z₁= Z₂ Re(Z₁) = Re (Z₂) -3x = 6 x = -2

and          Z₁ =Z₂1m(Z₁) = 1m(Z₂) 2y = -5 = -

Hence,    x = -2 and y =