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If z= 1- 2i then real part of z is |
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Answer» We know that Z=x+iy⇒∣z−1+2i∣=∣z+1−2i∣, locus of x=?⇒∣x+iy−1+2i∣=∣x+iy+1−2i∣⇒∣(x−1)+i(y+2)∣=∣(x+1)+i(y−2)∣⇒ (x−1) 2 +(y+2) 2 = (x+1) 2 +(y−2) 2 ⇒x 2 −2x+1+y 2 +4y+4=x 2 +2x+1+y 2 −4y+4⇒−2x+4y+5=2x−4y+5⇒4x=8y⇒x=2y∴x−2y=0∴ The locus of z is a straight LINE. HENCE, the answer straight line. |
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