Question

Let z1 = 2-i, z2 = -2+i. Find Re(z1z2)

Answer 1

Step-by-step explanation:

Re(z1)=2,Re(z2)=-2

Im(z1)=-1,Im(z2)=1

Re(z1z2)=Re(z1)Re(z2)-Im(z1)Im(z2)

=2.(-2)-(-1).1

=-3

Answer 2

Answer:

Given that :

z1 = 2 - i

z2 = -2 + i

To Find :

Re (z1z2)

Solution :

Finding : z1z2 = (2 - i)(-2 + i)

⇒ (-4 + 2i + 2i -i²)

⇒ (-4 + 4i + 1)

⇒ (4i - 3)

⇒ (-3 + 4i)

Hence, Re(z1z2) = -3.

Important :

• Negative numbers do not have square roots in the system of real numbers.
• The imaginary part of a number has iota.
• Iota or i = √-1.
• A complex number is the sum of a real number and an imaginary number.
• z = a + ib.
• The conjugate of a complex number is obtained by simply changing the sign of imaginary part.
• Modulus : |z| = √(x²+y²).