Question

for complex number z, the number of solutions of the equations z +z bar =6 and zzbar =25 is?
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Answer 1

Answer:

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Answer 2

The required solution is 3 + 4i

GIVEN: z + z bar = 6

            z. z bar = 25

TO FIND Solutions for the equations.

SOLUTION:

Let us assume z to be x+iy.

Therefore, the z bar is x-iy.

As we are given,

z + z bar = 6

(x + iy) + (x - iy) = 6

2x = 6

x = 3                                        -----Equation 1

Similarly,

z bar. z = 25

(x+iy) (x-iy) = 25

x² + y² = 25

From equation 1 we put x=3

3² + y² = 25

9 + y² = 25

y² = 25 - 9

y² = 16

y = 4

Therefore,

The required solution is x+iy = 3+4i.

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