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Question

3 - 4i equals


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Solution

Step 1: Compute the value of the complex expression

Given 3-4i
Let z=3-4i

|z|=32+42=5{|abi|=a2+b2}z=34i=reθ=arg&r=|z|θ=tan1ba=tan1(43)=πtan1(43){tan1(θ)=πtan1(θ)}θlies in the fourth quadrant.Argument=a=|πtan1(43)|z=re×z=5ei[πtan1(43)]
The value of the expression is z=5ei[πtan1(43)]


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