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Question

Question: The conjugate of \(x = 0,y = \frac{3 + 7i}{2i}\) in the form of a + ib, is....

The conjugate of x=0,y=3+7i2ix = 0,y = \frac{3 + 7i}{2i} in the form of a + ib, is.

A

1+2i1i\frac{1 + 2i}{1 - i}

B

11cosθ+isinθ\frac{1}{1 - \cos\theta + i\sin\theta}

C

(a+ib)<(c+id)(a + ib) < (c + id)

D

a2+b2=0a^{2} + b^{2} = 0

Answer

(a+ib)<(c+id)(a + ib) < (c + id)

Explanation

Solution

z=(2+i)23+iz = \frac { ( 2 + i ) ^ { 2 } } { 3 + i } z3=(3+5i)3=33+(5i)3+3.3.5i(3+5i)=198+10iz^{3} = (3 + 5i)^{3} = 3^{3} + (5i)^{3} + 3.3.5i(3 + 5i) = - 198 + 10i

Conjugate z3+zˉ+198=10i198+35i+198=3+5iz^{3} + \bar{z} + 198 = 10i - 198 + 3 - 5i + 198 = 3 + 5i.