Statement I If z1=a+i b and z2=c+i d be any two complex numbers, then the product z1 z2-(a c-b d)+i(a d+b c). Statement II Product of two complex numbers is also a complex number. Statement III (3+i 5)(2+i 6)=-24+i 28.

Question

Statement I If z1=a+i b and z2=c+i d be any two complex numbers, then the product z1 z2-(a c-b d)+i(a d+b c). Statement II Product of two complex numbers is also a complex number. Statement III (3+i 5)(2+i 6)=-24+i 28. (A) Statement I is true (B) Statement II is true (C) All are true (D) Neither I nor III is true

Tardigrade Admin · Accepted Answer

I. If z1=a+i b and z2=c+i d, then z1 z2 =(a+i b)(c+i d) =a c+i a d+i b c+i2 b d =(a c-b d)+i(a d+b c) (∵ i2=-1) Hence, Statement I is correct. II. Since, product of two complex numbers is also a complex number. This is called closure law of multiplication. i.e., If z1 and z2 are two complex numbers, then z1 ⋅ z2 is also a complex numbers. III. (3+5 i)(2+i 6)=(3 × 2-5 × 6)+i(3 × 6+5 × 2) =-24+i 28 Hence, all the statements are correct.

Q. Statement I If z1​=a+ib and z2​=c+id be any two complex numbers, then the product z1​z2​−(ac−bd)+i(ad+bc). Statement II Product of two complex numbers is also a complex number. Statement III (3+i5)(2+i6)=−24+i28.

Statement I is true

Statement II is true

All are true

Neither I nor III is true

Q. Statement I If $z_{1} = a + ib$ and $z_{2} = c + i d$ be any two complex numbers, then the product $z_{1} z_{2} - (a c - b d) + i (a d + b c)$ .
Statement II Product of two complex numbers is also a complex number.
Statement III $(3 + i 5) (2 + i 6) = - 24 + i 28$ .