# If is purely an imaginary number and z ≠ -1 then find the value of |z|.

Given: is purely imaginary number

Let z = x + iy

So,  Now, rationalizing the above by multiply and divide by the conjugate of [(x + 1) + iy]  Using (a – b)(a + b) = (a2 – b2)   Putting i2 = -1   Since, the number is purely imaginary it means real part is 0 x2 + y2 – 1 = 0

x2 + y2 = 1  |z| = 1

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Evaluate:

(i) (iii) .

RS Aggarwal - Mathematics