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Tips A5-line solutions comparing real and imaginary parts of both sides of the equation. Equality of complex numbers Let z1 = x1 + y1i, z2 = x2 + y2i. Complex numbers z1, z2 are equal, i.e. z1 = z2, if and only if Re (z1) = Re (z2), Im (z1) = Im (z2) or x1 = x2, y1 = y2 example If x + y =2-i, then x =2, y = -1.
the answer is:
z+3z=1+3i
so4z=1+3i
finaly z=1/4+3/4i
Let Z = x + iy,
Substitute in the equation z+3z=1+3i
x+iy+3(x+iy)=1+3i
x+iy+3x+3iy=1+3i
4x+4iy=1+3i
equating the real and imaginery parts, we get
4x=1,4iy=3i
x=1/4,y=3/4
z=1/4+3/4i
z+3z=1+3i
==>4z=1+3i
==> z=(1/4)+(3/4)i
==> Re(z)=1/4 and Im(z)=3/4
z=0.25+0.75 i
